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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
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 08/2018, Volume 376-377, pp. 238 - 246
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
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
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
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
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
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
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
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
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
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
Journal Article
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
Journal Article
Physica D: Nonlinear Phenomena, ISSN 0167-2789, 2008, Volume 237, Issue 10, pp. 1324 - 1333
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
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
Journal Article
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