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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
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
Journal of Differential Equations, ISSN 0022-0396, 2019, Volume 266, Issue 1, pp. 312 - 351
... x. By adding a small viscosity, one obtains a well posed parabolic equation. As the viscous term goes to zero, the uniqueness of the vanishing viscosity limit is proved... 
Conservation law with discontinuous flux | Regulated flux function | Hamilton–Jacobi equation | Existence and uniqueness | Vanishing viscosity | EXISTENCE | Hamilton-Jacobi equation | RESONANT SYSTEM | APPROXIMATION | ENTROPY CONDITIONS | EQUATIONS | CAUCHY-PROBLEM | UNIQUENESS | MATHEMATICS | DISCONTINUOUS FLUX | COEFFICIENTS | GRAVITATION | Environmental law
Journal Article
Mathematical Models and Methods in Applied Sciences, ISSN 0218-2025, 04/2013, Volume 23, Issue 4, pp. 565 - 616
We analyze a rate-independent model for damage evolution in elastic bodies. The central quantities are a stored energy functional and a dissipation functional,... 
Rate-independent damage evolution | vanishing viscosity method | arclength reparametrization | time discretization | EXISTENCE | MATHEMATICS, APPLIED | APPROXIMATION | SPACES | CRACK-PROPAGATION | EQUATIONS | NONLINEAR ELASTICITY | QUASI-STATIC EVOLUTION | SYSTEMS | FUNCTIONALS | PLASTICITY
Journal Article
SIAM journal on mathematical analysis, ISSN 1095-7154, 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
Mathematical Methods in the Applied Sciences, ISSN 0170-4214, 09/2017, Volume 40, Issue 14, pp. 5161 - 5176
Journal Article
Advances in mathematics (New York. 1965), 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
Nonlinearity, ISSN 0951-7715, 06/2015, Volume 28, Issue 6, pp. 1607 - 1631
This study considers the spatially periodic initial value problem of 2x2 quasi-linear parabolic systems in one space dimension having quadratic polynomial flux... 
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
European journal of applied mathematics, ISSN 0956-7925, 02/2019, Volume 30, Issue 1, pp. 117 - 175
This article is the third one in a series of papers by the authors on vanishing-viscosity solutions to rate-independent damage systems... 
Papers | Rate-independent damage system | Balanced Viscosity solutions | vanishing-viscosity approximation | MATHEMATICS, APPLIED | APPROXIMATION | EQUATIONS | BOUNDARY | LIMIT | MODEL | Viscosity | Knee | Boundary conditions | Parameterization | Damage
Journal Article
Journal of the European Mathematical Society, ISSN 1435-9855, 2016, Volume 18, Issue 9, pp. 2107 - 2165
J. Europ. Math. Soc. 18 (2016) 2107-2165 Balanced Viscosity solutions to rate-independent systems arise as limits of regularized rate-independent flows by adding a superlinear vanishing-viscosity dissipation... 
Energetic solutions | Existence results | Time discretization | Rate-independent systems | BV solutions | Vanishing viscosity | Mathematics - Analysis of PDEs
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 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
Journal of Differential Equations, ISSN 0022-0396, 2006, Volume 231, Issue 2, pp. 459 - 500
In this paper, using the vanishing viscosity method, we construct a solution of the Riemann problem for the system of conservation laws u t + ( u 2 ) x = 0 , v t + 2 ( u v ) x = 0 , w t + 2 ( v 2 + u w ) x... 
δ-Shocks | [formula omitted]-Shocks | Vacuum states | Systems of conservation laws | Vanishing viscosity method | Weak asymptotics method | Shocks | HYPERBOLIC SYSTEMS | delta '-shocks | MATHEMATICS | PRESSURE LIMIT | WAVES | vanishing viscosity method | systems of conservation laws | delta-shocks | CONSERVATION-LAWS | weak asymptotics method | WEAK SOLUTIONS | EULER EQUATIONS | PROPAGATION | vacuum states
Journal Article