Dynamical behaviors for 1D compressible Navier-Stokes equations with density-dependent viscosity

DOI10.1016/j.jde.2009.11.029zbMath1189.35388OpenAlexW1999064360MaRDI QIDQ963017

Zhen-Hua Guo, Ru-xu Lian, Hai-liang Li

Publication date: 8 April 2010

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

Full work available at URL: https://doi.org/10.1016/j.jde.2009.11.029

zbMATH Keywords

Navier-Stokes equationsfree boundarydynamical behaviorsdensity-dependent viscosity coefficient

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) Gas dynamics (general theory) (76N15) Navier-Stokes equations (35Q30) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Free boundary problems for PDEs (35R35) Weak solutions to PDEs (35D30)

Related Items (21)

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Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Global solutions of the Navier-Stokes equations for compressible flow with density-dependent viscosity and discontinuous initial data
• Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects
• On compressible Navier-Stokes equations with density dependent viscosities in bounded domains
• Global weak solutions to 1D compressible isentropic Navier-Stokes equations with density-dependent viscosity
• Lagrangian structure and propagation of singularities in multidimensional compressible flow
• One dimensional compressible Navier-Stokes equations with density dependent viscosity and free boundaries
• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations
• Solutions in the large for certain nonlinear parabolic systems
• 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
• 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
• On the Barotropic Compressible Navier–Stokes Equations
• On the asymptotic behavior of the one-dimensional motion of the polytropic ideal gas with stress-free condition
• Existence and Uniqueness of Global Strong Solutions for One-Dimensional Compressible Navier–Stokes Equations
• Spherically Symmetric Isentropic Compressible Flows with Density-Dependent Viscosity Coefficients
• Construction of solutions for compressible, isentropic Navier-Stokes equations in one space dimension with nonsmooth initial data
• 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
• Global Smooth Solutions of the Equations of a Viscous, Heat - Conducting, One - Dimensional Gas with Density - Dependent Viscosity
• 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
• VACUUM STATE FOR SPHERICALLY SYMMETRIC SOLUTIONS OF THE COMPRESSIBLE NAVIER–STOKES EQUATIONS
• Non-formation of vacuum states for compressible Navier-Stokes equations
• Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation

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