On classical solutions to 2D shallow water equations with degenerate viscosities

DOI10.1007/s00021-016-0276-3zbMath1369.35065arXiv1407.8471OpenAlexW2203360849MaRDI QIDQ2358740

Ronghua Pan, Shengguo Zhu, Ya-Chun Li

Publication date: 16 June 2017

Published in: Journal of Mathematical Fluid Mechanics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1407.8471

zbMATH Keywords

vacuumshallow water equationscompressible Navier-Stokes equationslocal well-posednessregular solutionsblow-up criteriondegenerate viscosity

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) Asymptotic behavior of solutions to PDEs (35B40) PDEs in connection with fluid mechanics (35Q35) Stability in context of PDEs (35B35) Hyperbolic conservation laws (35L65) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quantum hydrodynamics and relativistic hydrodynamics (76Y05) Galactic and stellar dynamics (85A05) Blow-up in context of PDEs (35B44)

Related Items (30)

Local Strong Solutions to the Full Compressible Navier--Stokes System with Temperature-Dependent Viscosity and Heat Conductivity ⋮ Existence of Global Classical Solutions for the Saint-Venant Equations ⋮ On the existence of local strong solutions to chemotaxis-shallow water system with large data and vacuum ⋮ Vanishing viscosity limit of the radiation hydrodynamic equations with far field vacuum ⋮ Existence for the compressible magnetohydrodynamic equations with vacuum ⋮ Vanishing viscosity limit of the rotating shallow water equations with far field vacuum ⋮ Global Regular Solutions for one-dimensional Degenerate Compressible Navier--Stokes Equations with Large Data and Far Field Vacuum ⋮ On the global-in-time inviscid limit of the 3D degenerate compressible Navier-Stokes equations ⋮ Finite-time blow-up of classical solutions to the rotating shallow water system with degenerate viscosity ⋮ Global large solutions to planar magnetohydrodynamics equations with temperature-dependent coefficients ⋮ Global well-posedness of regular solutions to the 1-D reduced gravity two-and-a-half layer model ⋮ Blow‐up criterion for compressible Navier–Stokes equations with degenerate viscosities ⋮ Singularity formation for the multi-dimensional compressible degenerate Navier-Stokes equations ⋮ Vanishing viscosity limit of the three-dimensional barotropic compressible Navier-Stokes equations with degenerate viscosities and far-field vacuum ⋮ Global existence of weak solutions to the Navier-Stokes-Korteweg equations ⋮ Global well-posedness and large-time behavior of classical solutions to the 3D Navier-Stokes system with changed viscosities ⋮ Existence results for the radiation hydrodynamic equations with degenerate viscosity coefficients and vacuum ⋮ Blow-up criterion for the 3D viscous polytropic fluids with degenerate viscosities ⋮ On the breakdown of regular solutions with finite energy for 3D degenerate compressible Navier-Stokes equations ⋮ Compressible fluids and active potentials ⋮ Well-posedness of the three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and far field vacuum ⋮ Existence of strong solutions to the rotating shallow water equations with degenerate viscosities ⋮ Global well-posedness of regular solutions to the three-dimensional isentropic compressible Navier-Stokes equations with degenerate viscosities and vacuum ⋮ On the existence of local classical solutions to the Navier-Stokes equations with degenerate viscosities ⋮ Vanishing viscosity limit of the Navier-Stokes equations to the Euler equations for compressible fluid flow with vacuum ⋮ On classical solutions for viscous polytropic fluids with degenerate viscosities and vacuum ⋮ On regular solutions and singularity formation for Vlasov/Navier-Stokes equations with degenerate viscosities and vacuum ⋮ Existence results for chemotaxis-shallow water system with degenerate viscosity coefficients and initial vacuum ⋮ On Classical Solutions of the Compressible Magnetohydrodynamic Equations with Vacuum ⋮ On regular solutions for three-dimensional full compressible Navier-Stokes equations with degenerate viscosities and far field vacuum

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Local existence of classical solutions to the two-dimensional viscous compressible flows with vacuum
• Two-velocity hydrodynamics in fluid mechanics. II. Existence of global \(\kappa\)-entropy solutions to the compressible Navier-Stokes systems with degenerate viscosities
• A blow-up criterion of strong solutions to the 2D compressible Navier-Stokes equations
• A Beale-Kato-Majda blow-up criterion for the 3-D compressible Navier-Stokes equations
• A vacuum problem for the one-dimensional compressible Navier-Stokes equations with density-dependent viscosity
• Large time asymptotics for partially dissipative hyperbolic systems
• Some diffusive capillary models of Korteweg type
• Existence results for viscous polytropic fluids with vacuum
• Derivation of a new two-dimensional viscous shallow water model with varying topography, bottom friction and capillary effects
• Mathematical justification of a shallow water model
• Blow-up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations
• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations
• Remarks on a paper by J. T. Beale, T. Kato, and A. Majda (Remarks on the breakdown of smooth solutions for the 3-dimensional Euler equations)
• Formation of singularities in three-dimensional compressible fluids
• Compact sets in the space \(L^ p(0,T;B)\)
• The initial value problem for the equations of motion of viscous and heat-conductive gases
• Global existence for the Cauchy problem for the viscous shallow water equations
• Compressible Euler equations with vacuum
• 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
• Semi-Galerkin approximation and strong solutions to the equations of the nonhomogeneous asymmetric fluids.
• Unique solvability of the initial boundary value problems for compressible viscous fluids.
• Global existence for the Dirichlet problem for the viscous shallow water equations
• On blowup of classical solutions to the compressible Navier-Stokes equations
• Formation of singularities in solutions to the compressible radiation hydrodynamics equations with vacuum
• On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities
• The Cauchy problem for viscous shallow water equations
• LOCAL THEORY IN CRITICAL SPACES FOR COMPRESSIBLE VISCOUS AND HEAT-CONDUCTIVE GASES
• Mathematical derivation of viscous shallow-water equations with zero surface tension
• Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations
• CAUCHY PROBLEM FOR VISCOUS SHALLOW WATER EQUATIONS WITH A TERM OF CAPILLARITY
• On the Well-Posedness for the Viscous Shallow Water Equations
• Sur la solution à support compact de l’equation d’Euler compressible
• The Failure of Continuous Dependence on Initial data for the Navier–Stokes equations of Compressible Flow
• Blowup of smooth solutions to the compressible Navier-Stokes equation with compact density
• On Some Compressible Fluid Models: Korteweg, Lubrication, and Shallow Water Systems
• Recent Mathematical Results and Open Problems about Shallow Water Equations
• Well-Posedness in Critical Spaces for Barotropic Viscous Fluids with Truly Not Constant Density
• Le problème de Cauchy pour les équations différentielles d'un fluide général
• Derivation of viscous Saint-Venant system for laminar shallow water; numerical validation

This page was built for publication: On classical solutions to 2D shallow water equations with degenerate viscosities