On the dynamics of Navier-Stokes equations for a shallow water model

DOI10.1016/j.jde.2011.01.010zbMath1215.35172OpenAlexW2009237561MaRDI QIDQ631876

Qin Duan

Publication date: 14 March 2011

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2011.01.010

zbMATH Keywords

vacuumcompressible Navier-Stokes equationsfree boundarydensity-dependent viscosityshallow water model

Mathematics Subject Classification ID

Asymptotic behavior of solutions to PDEs (35B40) Stability in context of PDEs (35B35) Water waves, gravity waves; dispersion and scattering, nonlinear interaction (76B15) Navier-Stokes equations (35Q30) Free boundary problems for PDEs (35R35) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

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Cites Work

• Free boundary problem for the equation of spherically symmetric motion of viscous gas
• A vacuum problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity
• Free boundary problem for one-dimensional motions of compressible gas and vacuum
• On global motions of a compressible barotropic and self-gravitating gas with density-dependent viscosities
• Global weak solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity
• The Cauchy problem for 1D compressible flows with density-dependent viscosity coefficients
• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations
• The initial value problem for the equations of motion of viscous and heat-conductive gases
• Solvability in the large of a system of equations of the one- dimensional motion of an inhomogeneous viscous heat-conducting gas
• Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas
• Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum
• Compressible Navier-Stokes equations with degenerate viscosity coefficient and vacuum. II
• Existence of global weak solutions for a 2D viscous shallow water equations and convergence to the quasi-geostrophic model
• Vacuum states for compressible flow
• Global behavior of compressible Navier-Stokes equations with a degenerate viscosity coefficient
• COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY AND VACUUM
• Navier–Stokes equations with degenerate viscosity, vacuum and gravitational force
• On the Barotropic Compressible Navier–Stokes Equations
• Existence and Uniqueness of Global Strong Solutions for One-Dimensional Compressible Navier–Stokes Equations
• Spherically Symmetric Isentropic Compressible Flows with Density-Dependent Viscosity Coefficients
• Global Existence for 1D, Compressible, Isentropic Navier-Stokes Equations with Large Initial Data
• The Failure of Continuous Dependence on Initial data for the Navier–Stokes equations of Compressible Flow
• Les solutions à support compact de l’équation du mouvement des atmosphères d’étoiles
• Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density
• Interface Behavior of Compressible Navier--Stokes Equations with Vacuum
• On Some Compressible Fluid Models: Korteweg, Lubrication, and Shallow Water Systems
• Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation
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