Short-Time Stability of Scalar Viscous Shocks in the Inviscid Limit by the Relative Entropy Method
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Publication:5253464
DOI10.1137/140961523zbMath1316.35195arXiv1210.7853OpenAlexW2007470318MaRDI QIDQ5253464
Kyudong Choi, Alexis F. Vasseur
Publication date: 26 May 2015
Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1210.7853
Asymptotic behavior of solutions to PDEs (35B40) Shocks and singularities for hyperbolic equations (35L67) Stability in context of PDEs (35B35) Hyperbolic conservation laws (35L65)
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Cites Work
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- Relative entropy and the stability of shocks and contact discontinuities for systems of conservation laws with non-\(BV\) perturbations
- \(L ^{2}\) stability estimates for shock solutions of scalar conservation laws using the relative entropy method
- The second law of thermodynamics and stability
- Viscous limits for piecewise smooth solutions to systems of conservation laws
- Large-time behavior of entropy solutions of conservation laws
- Divergence-measure fields and hyperbolic conservation laws
- The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels
- Convergence of solutions to the Boltzmann equation in the incompressible Euler limit
- Well-posedness for hyperbolic systems of conservation laws with large BV data
- \(L^1\) stability estimates for \(n\times n\) conservation laws
- Uniqueness and stability of Riemann solutions with large oscillation in gas dynamics
- Relative entropy and hydrodynamics of Ginzburg-Landau models
- From discrete velocity Boltzmann equations to gas dynamics before shocks
- Relative entropy in hyperbolic relaxation
- Asymptotic analysis for a Vlasov-Fokker-Planck compressible Navier-Stokes system of equations
- Rate of Convergence for Vanishing Viscosity Approximations to Hyperbolic Balance Laws
- Accuracy of some approximate methods for computing the weak solutions of a first-order quasi-linear equation
- Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
- ?1 stability of shock waves in scalar viscous conservation laws
- From the BGK model to the Navier–Stokes equations
- From the Boltzmann equation to the Stokes-Fourier system in a bounded domain
- On the convergence rate of vanishing viscosity approximations
- From Kinetic Equations to Multidimensional Isentropic Gas Dynamics Before Shocks
- Asymptotic stability and Liouville theorem for scalar viscous conservation laws in cylinders
- The partial differential equation ut + uux = μxx
- From the Boltzmann equations to the equations of incompressible fluid mechanics. I, II
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