Physica D: Nonlinear Phenomena, ISSN 0167-2789, 08/2018, Volume 376-377, pp. 31 - 38

.... We show that the damped Euler system has a (strong) global attractor in H1(Ω). We also show that in the vanishing viscosity limit the global attractors of the Navier...

Vanishing viscosity limit | Damped Euler equations | Global attractors | EXISTENCE | MATHEMATICS, APPLIED | TRAJECTORY ATTRACTORS | PHYSICS, MULTIDISCIPLINARY | SPATIALLY NONDECAYING SOLUTIONS | EQUATIONS | PHYSICS, MATHEMATICAL | UNIQUENESS | SEMIGROUPS | DISSIPATIVE 2D EULER | R-2 | DOMAINS | STRONG-CONVERGENCE | Mathematics - Analysis of PDEs

Vanishing viscosity limit | Damped Euler equations | Global attractors | EXISTENCE | MATHEMATICS, APPLIED | TRAJECTORY ATTRACTORS | PHYSICS, MULTIDISCIPLINARY | SPATIALLY NONDECAYING SOLUTIONS | EQUATIONS | PHYSICS, MATHEMATICAL | UNIQUENESS | SEMIGROUPS | DISSIPATIVE 2D EULER | R-2 | DOMAINS | STRONG-CONVERGENCE | Mathematics - Analysis of PDEs

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 08/2018, Volume 376-377, pp. 238 - 246

In this paper, we are concerned with the vanishing viscosity problem for the three-dimensional Navier...

Navier–Stokes equations | Vanishing viscosity limit | Euler equations | Helical symmetry | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | PHYSICS, MULTIDISCIPLINARY | REGULARITY | 3-DIMENSIONAL EULER EQUATIONS | WEAK SOLUTIONS | PHYSICS, MATHEMATICAL | Navier-Stokes equations | Mathematics - Analysis of PDEs

Navier–Stokes equations | Vanishing viscosity limit | Euler equations | Helical symmetry | MATHEMATICS, APPLIED | GLOBAL EXISTENCE | PHYSICS, MULTIDISCIPLINARY | REGULARITY | 3-DIMENSIONAL EULER EQUATIONS | WEAK SOLUTIONS | PHYSICS, MATHEMATICAL | Navier-Stokes equations | Mathematics - Analysis of PDEs

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 06/2019, Volume 266, Issue 12, pp. 8110 - 8163

.... We focus on the one dimensional (planar) version of the model and address the problem of well posedness as well as convergence of the sequence of solutions as the bulk viscosity tends to zero together with some other interaction parameters...

Compressible MHD planar equations | Vanishing viscosity | Nonlinear Schrödinger equation | MATHEMATICS | Nonlinear Schrodinger equation | ISENTROPIC GAS-DYNAMICS | CONVERGENCE | SYSTEMS | EULER EQUATIONS

Compressible MHD planar equations | Vanishing viscosity | Nonlinear Schrödinger equation | MATHEMATICS | Nonlinear Schrodinger equation | ISENTROPIC GAS-DYNAMICS | CONVERGENCE | SYSTEMS | EULER EQUATIONS

Journal Article

Transactions of the American Mathematical Society, ISSN 0002-9947, 03/2017, Volume 369, Issue 3, pp. 2003 - 2027

Whether, in the presence of a boundary, solutions of the Navier-Stokes equations converge to a solution to the Euler equations in the vanishing viscosity limit is unknown...

Boundary layer theory | Vanishing viscosity | boundary layer theory | MATHEMATICS | NAVIER-STOKES EQUATIONS | APPROXIMATION | BOUNDARY-LAYERS | PLANE | FLOWS | VORTICITY | INVISCID LIMIT

Boundary layer theory | Vanishing viscosity | boundary layer theory | MATHEMATICS | NAVIER-STOKES EQUATIONS | APPROXIMATION | BOUNDARY-LAYERS | PLANE | FLOWS | VORTICITY | INVISCID LIMIT

Journal Article

SIAM JOURNAL ON MATHEMATICAL ANALYSIS, ISSN 0036-1410, 2019, Volume 51, Issue 3, pp. 2168 - 2205

We prove the convergence of the vanishing viscosity limit of the one-dimensional, isentropic, compressible Navier-Stokes equations to the isentropic Euler equations in the case of a general pressure law...

EXISTENCE | compensated compactness | MATHEMATICS, APPLIED | relative finite-energy | STABILITY | ISENTROPIC GAS-DYNAMICS | CONVERGENCE | vanishing viscosity | Euler equations | FLOW | Navier-Stokes equations | FRIEDRICHS SCHEME

EXISTENCE | compensated compactness | MATHEMATICS, APPLIED | relative finite-energy | STABILITY | ISENTROPIC GAS-DYNAMICS | CONVERGENCE | vanishing viscosity | Euler equations | FLOW | Navier-Stokes equations | FRIEDRICHS SCHEME

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2017, Volume 40, Issue 14, pp. 5161 - 5176

In this paper, we consider the inviscid limit for the periodic solutions to Navier...

vanishing viscosity limit | incompressible Navier–Stokes equation | Gevrey class | incompressible Navier-Stokes equation | SYSTEM | MATHEMATICS, APPLIED | CLASS REGULARITY | WELL-POSEDNESS | ANALYTICITY | 3-DIMENSIONAL EULER EQUATIONS | HALF-SPACE | BOUNDARY | INITIAL DATA | PRANDTL EQUATION | Fluid dynamics | Viscosity | Life span | Fluid flow | Navier Stokes equations | Stokes law (fluid mechanics) | Navier-Stokes equations | Convergence | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

vanishing viscosity limit | incompressible Navier–Stokes equation | Gevrey class | incompressible Navier-Stokes equation | SYSTEM | MATHEMATICS, APPLIED | CLASS REGULARITY | WELL-POSEDNESS | ANALYTICITY | 3-DIMENSIONAL EULER EQUATIONS | HALF-SPACE | BOUNDARY | INITIAL DATA | PRANDTL EQUATION | Fluid dynamics | Viscosity | Life span | Fluid flow | Navier Stokes equations | Stokes law (fluid mechanics) | Navier-Stokes equations | Convergence | Mathematics - Analysis of PDEs | Analysis of PDEs | Mathematics

Journal Article

Journal of Functional Analysis, ISSN 0022-1236, 11/2019, Volume 277, Issue 10, pp. 3599 - 3652

.... In this paper we study the vanishing viscosity limit of sequences of these solutions. As the viscosity tends to zero, some sequences of solutions Clocm converge to solutions...

Stationary Navier-Stokes equations | Vanishing viscosity limit | Homogeneous axisymmetric no-swirl solutions | SIMILAR VISCOUS FLOWS | ANALYTIC SOLUTIONS | MATHEMATICS | ISOLATED SINGULARITIES | AXIAL CAUSES | HALF-SPACE | EULER | INVISCID LIMIT | Fluid dynamics

Stationary Navier-Stokes equations | Vanishing viscosity limit | Homogeneous axisymmetric no-swirl solutions | SIMILAR VISCOUS FLOWS | ANALYTIC SOLUTIONS | MATHEMATICS | ISOLATED SINGULARITIES | AXIAL CAUSES | HALF-SPACE | EULER | INVISCID LIMIT | Fluid dynamics

Journal Article

Nonlinearity, ISSN 0951-7715, 06/2015, Volume 28, Issue 6, pp. 1607 - 1631

.... The study concentrates on scaled spatially 2p-periodic solutions as the dissipation vanishes, and in particular the behaviour of such limits when generalized...

vanishing viscosity limit | high-order dissipation | mixed hyperbolic-elliptic systems | MATHEMATICS, APPLIED | WAVES | INSTABILITY | FLUID | REGIONS | EQUATIONS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | Nonlinear dynamics | Multilayers | Mathematical analysis | Dissipation | Nonlinearity | Polynomials | Channel flow | Dynamical systems

vanishing viscosity limit | high-order dissipation | mixed hyperbolic-elliptic systems | MATHEMATICS, APPLIED | WAVES | INSTABILITY | FLUID | REGIONS | EQUATIONS | CONSERVATION-LAWS | PHYSICS, MATHEMATICAL | Nonlinear dynamics | Multilayers | Mathematical analysis | Dissipation | Nonlinearity | Polynomials | Channel flow | Dynamical systems

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 05/2013, Volume 254, Issue 10, pp. 4122 - 4143

For a Hamilton–Jacobi equation defined on a network, we introduce its vanishing viscosity approximation...

Maximum principle | Hamilton–Jacobi equation | Viscosity solution | Vanishing viscosity | Network | Hamilton-Jacobi equation | MATHEMATICS | DIFFUSION-PROCESSES | PRINCIPLE | GRAPHS

Maximum principle | Hamilton–Jacobi equation | Viscosity solution | Vanishing viscosity | Network | Hamilton-Jacobi equation | MATHEMATICS | DIFFUSION-PROCESSES | PRINCIPLE | GRAPHS

Journal Article

Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 12/2017, Volume 40, Issue 18, pp. 7564 - 7597

We investigate the uniform regularity and vanishing viscosity limit for the incompressible chemotaxis‐Navier...

vanishing viscosity limit | conormal Sobolev space | Navier boundary condition | incompressible chemotaxis‐Navier‐Stokes system | Conormal Sobolev space | Vanishing viscosity limit | Incompressible chemotaxis-Navier-Stokes system | EXISTENCE | MATHEMATICS, APPLIED | EQUATIONS | VORTICITY | INVISCID LIMIT | ANALYTIC SOLUTIONS | incompressible chemotaxis-Navier-Stokes system | FLUID MODEL | HALF-SPACE | FLOWS | Fluid dynamics | Viscosity | Sobolev space | Fluid flow | Boundary conditions | Regularity | Stokes law (fluid mechanics) | Navier-Stokes equations | Mathematics - Analysis of PDEs

vanishing viscosity limit | conormal Sobolev space | Navier boundary condition | incompressible chemotaxis‐Navier‐Stokes system | Conormal Sobolev space | Vanishing viscosity limit | Incompressible chemotaxis-Navier-Stokes system | EXISTENCE | MATHEMATICS, APPLIED | EQUATIONS | VORTICITY | INVISCID LIMIT | ANALYTIC SOLUTIONS | incompressible chemotaxis-Navier-Stokes system | FLUID MODEL | HALF-SPACE | FLOWS | Fluid dynamics | Viscosity | Sobolev space | Fluid flow | Boundary conditions | Regularity | Stokes law (fluid mechanics) | Navier-Stokes equations | Mathematics - Analysis of PDEs

Journal Article

Journal of Mathematical Analysis and Applications, ISSN 0022-247X, 2011, Volume 384, Issue 2, pp. 232 - 245

In this paper, we study the vanishing viscosity limit for a coupled Navier–Stokes/Allen–Cahn system in a bounded domain...

Navier–Stokes | Vanishing viscosity limit | Euler | Allen–Cahn | Navier-Stokes | Allen-Cahn | FLUIDS | MATHEMATICS | MATHEMATICS, APPLIED | LIQUID-CRYSTALS | EQUATIONS | FLOWS | Fluid dynamics

Navier–Stokes | Vanishing viscosity limit | Euler | Allen–Cahn | Navier-Stokes | Allen-Cahn | FLUIDS | MATHEMATICS | MATHEMATICS, APPLIED | LIQUID-CRYSTALS | EQUATIONS | FLOWS | Fluid dynamics

Journal Article

Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 2019, Volume 29, Issue 6

.... Firstly, the global existence of strong solution for large initial data is obtained, and then the limit of the vanishing shear viscosity is justified...

global existence | vanishing shear viscosity | MHD system | boundary layer | EXISTENCE | MATHEMATICS, APPLIED | ONE-DIMENSIONAL EQUATIONS | NAVIER-STOKES EQUATIONS | FLOWS | GLOBAL-SOLUTIONS

global existence | vanishing shear viscosity | MHD system | boundary layer | EXISTENCE | MATHEMATICS, APPLIED | ONE-DIMENSIONAL EQUATIONS | NAVIER-STOKES EQUATIONS | FLOWS | GLOBAL-SOLUTIONS

Journal Article

Acta Applicandae Mathematicae, ISSN 0167-8019, 2/2018, Volume 153, Issue 1, pp. 101 - 124

...Acta Appl Math (2018) 153:101–124 DOI 10.1007/s10440-017-0122-5 L -Splines and Viscosity Limits for Well-Balanced Schemes Acting on Linear Parabolic Equations...

34D15 | Fundamental system of solutions | Theoretical, Mathematical and Computational Physics | Complex Systems | Monotone well-balanced scheme | 65M06 | Classical Mechanics | Mathematics | Constant/Line Perturbation method (C/L-PM) | Parabolic Cylinder functions (PCF) | 76R50 | 76M45 | Vanishing viscosity | Mathematics, general | Computer Science, general | ℒ-spline | MATHEMATICS, APPLIED | SINGULAR PERTURBATION PROBLEM | NUMERICAL-METHOD | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | WEAK VARIATIONAL FORMULATION | SOURCE TERMS | DISCRETIZATION | CYLINDER FUNCTIONS | SCALAR CONSERVATION-LAWS | DIFFUSION | L-spline | Viscosity | Boundary value problems | Kinetic equations | Splines | Asymptotic properties | Mathematical analysis | Numerical methods | Computational grids | Regularity | Finite difference method | Knots

34D15 | Fundamental system of solutions | Theoretical, Mathematical and Computational Physics | Complex Systems | Monotone well-balanced scheme | 65M06 | Classical Mechanics | Mathematics | Constant/Line Perturbation method (C/L-PM) | Parabolic Cylinder functions (PCF) | 76R50 | 76M45 | Vanishing viscosity | Mathematics, general | Computer Science, general | ℒ-spline | MATHEMATICS, APPLIED | SINGULAR PERTURBATION PROBLEM | NUMERICAL-METHOD | BOUNDARY-VALUE-PROBLEMS | DIFFERENTIAL-EQUATIONS | WEAK VARIATIONAL FORMULATION | SOURCE TERMS | DISCRETIZATION | CYLINDER FUNCTIONS | SCALAR CONSERVATION-LAWS | DIFFUSION | L-spline | Viscosity | Boundary value problems | Kinetic equations | Splines | Asymptotic properties | Mathematical analysis | Numerical methods | Computational grids | Regularity | Finite difference method | Knots

Journal Article

Advances in Mathematics, ISSN 0001-8708, 2006, Volume 203, Issue 2, pp. 497 - 513

In this paper, we prove the global in time regularity for the 2D Boussinesq system with either the zero diffusivity or the zero viscosity...

Vanishing viscosity limit | Boussinesq equations | Global regularity | Vanishing diffusivity limit | vanishing viscosity limit | MATHEMATICS | vanishing diffusivity limit | BLOW-UP CRITERION | global regularity | LOCAL EXISTENCE

Vanishing viscosity limit | Boussinesq equations | Global regularity | Vanishing diffusivity limit | vanishing viscosity limit | MATHEMATICS | vanishing diffusivity limit | BLOW-UP CRITERION | global regularity | LOCAL EXISTENCE

Journal Article

SIAM Journal on Mathematical Analysis, ISSN 0036-1410, 2015, Volume 47, Issue 6, pp. 4123 - 4191

...-slip boundary conditions in an interval of time which is uniform in the vanishing viscosity limit. The solution is uniformly bounded in a conormal Sobolev space and is uniformly bounded in W-1,W-infinity...

Convergence rate | Vanishing viscosity limit | Euler equations | Compressible Navier-Stokes | compressible Navier-Stokes | vanishing viscosity limit | ANALYTIC SOLUTIONS | MATHEMATICS, APPLIED | PLANE | EQUATIONS | HALF-SPACE | convergence rate | EULER | INVISCID LIMIT

Convergence rate | Vanishing viscosity limit | Euler equations | Compressible Navier-Stokes | compressible Navier-Stokes | vanishing viscosity limit | ANALYTIC SOLUTIONS | MATHEMATICS, APPLIED | PLANE | EQUATIONS | HALF-SPACE | convergence rate | EULER | INVISCID LIMIT

Journal Article

Acta Applicandae Mathematicae, ISSN 0167-8019, 6/2018, Volume 155, Issue 1, pp. 151 - 175

By the vanishing viscosity approach, a class of non-strictly hyperbolic systems of conservation laws that contain the equations of geometrical optics as a prototype are studied...

Computational Mathematics and Numerical Analysis | Delta shock wave | Generalized vacuum state | Calculus of Variations and Optimal Control; Optimization | Vanishing viscosity method | Probability Theory and Stochastic Processes | Mathematics | Applications of Mathematics | System of conservation law | Partial Differential Equations | FLUIDS | MATHEMATICS, APPLIED | DELTA-SHOCK-WAVES | FLUX-APPROXIMATION | PRESSURE LIMIT | VACUUM STATES | ISENTROPIC GAS-DYNAMICS | RELATIVISTIC EULER EQUATIONS | CONSERVATION-LAWS | GENERALIZED SOLUTIONS | Environmental law | Viscosity | Conservation laws | Shock waves | Geometrical optics | Hyperbolic systems | Uniqueness

Computational Mathematics and Numerical Analysis | Delta shock wave | Generalized vacuum state | Calculus of Variations and Optimal Control; Optimization | Vanishing viscosity method | Probability Theory and Stochastic Processes | Mathematics | Applications of Mathematics | System of conservation law | Partial Differential Equations | FLUIDS | MATHEMATICS, APPLIED | DELTA-SHOCK-WAVES | FLUX-APPROXIMATION | PRESSURE LIMIT | VACUUM STATES | ISENTROPIC GAS-DYNAMICS | RELATIVISTIC EULER EQUATIONS | CONSERVATION-LAWS | GENERALIZED SOLUTIONS | Environmental law | Viscosity | Conservation laws | Shock waves | Geometrical optics | Hyperbolic systems | Uniqueness

Journal Article

17.
Full Text
Limit of viscous dynamic processes in delamination as the viscosity and inertia vanish

ESAIM - Control, Optimisation and Calculus of Variations, ISSN 1292-8119, 04/2017, Volume 23, Issue 2, pp. 593 - 625

.... In the one-dimensional case we give a more detailed description of the limit evolution and we show that it behaves in a very similar way to the limit of the solutions of the dynamic model in [T. Roubicek, SIAM J. Math. Anal. 45 (2013) 101-126], where no viscosity in the adhesive is taken into account.

Delamination | Contact mechanics | Hyperbolic PDEs systems | Vanishing viscosity | Visco-elasticity | delamination | FRICTION | MATHEMATICS, APPLIED | hyperbolic PDEs systems | contact mechanics | vanishing viscosity | MODEL | DAMAGE | VISCOELASTIC BODIES | QUASI-STATIC EVOLUTION | ADHESIVE CONTACT | AUTOMATION & CONTROL SYSTEMS | RATE-INDEPENDENT SYSTEMS | PLASTICITY | Viscoelasticity | Viscosity | Evolution | Dynamic models | Elastic bodies

Delamination | Contact mechanics | Hyperbolic PDEs systems | Vanishing viscosity | Visco-elasticity | delamination | FRICTION | MATHEMATICS, APPLIED | hyperbolic PDEs systems | contact mechanics | vanishing viscosity | MODEL | DAMAGE | VISCOELASTIC BODIES | QUASI-STATIC EVOLUTION | ADHESIVE CONTACT | AUTOMATION & CONTROL SYSTEMS | RATE-INDEPENDENT SYSTEMS | PLASTICITY | Viscoelasticity | Viscosity | Evolution | Dynamic models | Elastic bodies

Journal Article

Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2008, Volume 237, Issue 10, pp. 1324 - 1333

...–Stokes solutions converge strongly in L 2 to the corresponding stationary solution of the Euler equations when viscosity vanishes...

Rotating boundary | Vanishing viscosity limit | Euler and Navier–Stokes | Circular symmetry | Boundary layer | Euler and Navier-Stokes | FLUIDS | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | BOUNDARY-CONDITIONS | boundary layer | PHYSICS, MATHEMATICAL | rotating boundary | LAYERS | vanishing viscosity limit | ANALYTIC SOLUTIONS | NAVIER-STOKES EQUATIONS | circular symmetry | HALF-SPACE | EULER

Rotating boundary | Vanishing viscosity limit | Euler and Navier–Stokes | Circular symmetry | Boundary layer | Euler and Navier-Stokes | FLUIDS | MATHEMATICS, APPLIED | PHYSICS, MULTIDISCIPLINARY | BOUNDARY-CONDITIONS | boundary layer | PHYSICS, MATHEMATICAL | rotating boundary | LAYERS | vanishing viscosity limit | ANALYTIC SOLUTIONS | NAVIER-STOKES EQUATIONS | circular symmetry | HALF-SPACE | EULER

Journal Article

Journal of Differential Equations, ISSN 0022-0396, 11/2019, Volume 267, Issue 11, pp. 6216 - 6264

In this paper we study the vanishing inertia and viscosity limit of a second order system set in an Euclidean space, driven by a possibly nonconvex time-dependent potential satisfying very general assumptions...

Singular perturbations | Vanishing inertia and viscosity limit | Variational methods | Balanced Viscosity solutions | Quasi static limit | MATHEMATICS | SYSTEMS | VISCOSITY | GRADIENT FLOWS | PEELING TEST | PLASTICITY

Singular perturbations | Vanishing inertia and viscosity limit | Variational methods | Balanced Viscosity solutions | Quasi static limit | MATHEMATICS | SYSTEMS | VISCOSITY | GRADIENT FLOWS | PEELING TEST | PLASTICITY

Journal Article

Mathematische Annalen, ISSN 0025-5831, 8/2016, Volume 365, Issue 3, pp. 1527 - 1557

.... The domain is the exterior of a regular lattice of rigid particles. We study the simultaneous limit of vanishing particle size and distance, and of vanishing viscosity...

Mathematics, general | 76S05 | Mathematics | 35Q31 | 35Q30 | MATHEMATICS | VISCOUS INCOMPRESSIBLE FLUID | DOMAIN | ILL-POSEDNESS | SMALL OBSTACLE | FLOW | HOMOGENIZATION | PRANDTL EQUATION | Fluid dynamics | Analysis | Analysis of PDEs

Mathematics, general | 76S05 | Mathematics | 35Q31 | 35Q30 | MATHEMATICS | VISCOUS INCOMPRESSIBLE FLUID | DOMAIN | ILL-POSEDNESS | SMALL OBSTACLE | FLOW | HOMOGENIZATION | PRANDTL EQUATION | Fluid dynamics | Analysis | Analysis of PDEs

Journal Article

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