Global classical solution to the three-dimensional isentropic compressible Navier-Stokes equations with general initial data

DOI10.1007/s11425-012-4481-0zbMath1302.35314OpenAlexW2080771446MaRDI QIDQ1934393

Jun Ning Zhao, Xue-Mei Deng, Peixin Zhang

Publication date: 28 January 2013

Published in: Science China. Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11425-012-4481-0

zbMATH Keywords

compressible Navier-Stokes equationsglobal classical solutionslarge viscosity coefficient

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) PDEs of mixed type (35M10) Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs (35B30) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02) Classical solutions to PDEs (35A09)

Related Items (7)

Global classical solutions of compressible isentropic Navier-Stokes equations with small density ⋮ Global classical solutions to the 2D compressible Navier-Stokes equations with vacuum ⋮ Global well-posedness of the strong solutions to the two-dimensional full compressible magnetohydrodynamics equations with large viscosity ⋮ Existence and uniqueness of global classical solutions to 3D isentropic compressible Navier-Stokes equations with general initial data ⋮ Global classical solutions of 3D isentropic compressible MHD with general initial data ⋮ Global strong solution to the two-dimensional full compressible Navier-Stokes equations with large viscosity ⋮ Global classical solution to the 3D isentropic compressible Navier-Stokes equations with general initial data and a density-dependent viscosity coefficient

Cites Work

• A Beale-Kato-Majda blow-up criterion for the 3-D compressible Navier-Stokes equations
• On the uniqueness of compressible fluid motions
• Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases
• Local well-posedness of lower regularity solutions for the incompressible viscoelastic fluid system
• The initial value problem for the equations of motion of viscous and heat-conductive gases
• Unique solvability of the initial boundary value problems for compressible viscous fluids.
• Strong solutions of the Navier-Stokes equations for isentropic compressible fluids
• Global solutions of the Navier-Stokes equations for multidimensional compressible flow with discontinuous initial data
• Strong convergence to global solutions for multidimensional flows of compressible, viscous fluids with polytropic equations of state and discontinuous initial data
• On classical solutions of the compressible Navier-Stokes equations with nonnegative initial densities
• Global well-posedness of classical solutions with large oscillations and vacuum to the three-dimensional isentropic compressible Navier-Stokes equations
• Global Existence for 1D, Compressible, Isentropic Navier-Stokes Equations with Large Initial Data
• Uniform estimates and stabilization of symmetric solutions of a system of quasilinear equations
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