Shallow water equations: viscous solutions and inviscid limit

DOI10.1007/s00033-012-0209-9zbMath1388.35124OpenAlexW2036636990WikidataQ57386460 ScholiaQ57386460MaRDI QIDQ1925824

Mikhail Perepelitsa, Gui-Qiang G. Chen

Publication date: 19 December 2012

Published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00033-012-0209-9

zbMATH Keywords

entropyfrictionshallow water equationsuniform estimatesentropy solutionsinviscid limitmeasure-valued solutionsfinite energyviscousinviscidSaint-Venant systementropy fluxentropy dissipation measuresviscous solutions\(H^{-1}\)-compactness

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) Singular perturbations in context of PDEs (35B25) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Navier-Stokes equations (35Q30) First-order nonlinear hyperbolic equations (35L60) Hyperbolic conservation laws (35L65) Initial value problems for first-order hyperbolic systems (35L45) Viscous-inviscid interaction for compressible fluids and gas dynamics (76N17) Degenerate hyperbolic equations (35L80) Viscous-inviscid interaction (76D09) Viscosity solutions to PDEs (35D40) Euler equations (35Q31)

Related Items (7)

Vanishing viscosity limit for Navier–Stokes equations with general viscosity to Euler equations ⋮ Modeling shallow water waves ⋮ Asymptotics of the 1D compressible Navier-Stokes equations with density-dependent viscosity ⋮ Quasilinear viscous approximations to scalar conservation laws ⋮ Inviscid limit for the damped Boussinesq equation ⋮ Weak continuity and compactness for nonlinear partial differential equations ⋮ Global solutions of the compressible Euler equations with large initial data of spherical symmetry and positive far-field density

Cites Work

• Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics
• Convergence of the viscosity method for isentropic gas dynamics
• Finite energy solutions to the isentropic Euler equations with geometric effects
• Global solutions of the equations of one-dimensional, compressible flow with large data and forces, and with differing end states
• Kinetic formulation of the isentropic gas dynamics and \(p\)-systems
• Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model
• Existence theory for the isentropic Euler equations
• Compressible Euler equations with general pressure law
• On the Barotropic Compressible Navier–Stokes Equations
• Vanishing viscosity limit of the Navier-Stokes equations to the euler equations for compressible fluid flow
• Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation
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