Global Well-Posedness of Classical Solutions to the Cauchy Problem of Two-Dimensional Barotropic Compressible Navier--Stokes System with Vacuum and Large Initial Data

DOI10.1137/21M1440943zbMath1491.35338arXiv1207.3746OpenAlexW4281560645MaRDI QIDQ5081158

Xiangdi Huang, Jing Li

Publication date: 13 June 2022

Published in: SIAM Journal on Mathematical Analysis (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1207.3746

zbMATH Keywords

vacuumCauchy problemcompressible Navier-Stokes equationsglobal classical solutionslarge initial data

Mathematics Subject Classification ID

Smoothness and regularity of solutions to PDEs (35B65) PDEs in connection with fluid mechanics (35Q35) 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) Strong solutions to PDEs (35D35) Classical solutions to PDEs (35A09)

Related Items

Analytical solutions to the 3-D compressible Navier-Stokes equations with free boundaries, Blow up criteria for the 2D compressible Navier-Stokes equations in bounded domains with vacuum, Global solutions of 3D isentropic compressible Navier-Stokes equations with two slow variables, On the global solvability of the coupled kinetic-fluid system for flocking with large initial data, Global existence of strong solution for viscous shallow water system with large initial data on the irrotational part

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence and blowup behavior of global strong solutions to the two-dimensional barotropic compressible Navier-Stokes system with vacuum and large initial data
• On local classical solutions to the Cauchy problem of the two-dimensional barotropic compressible Navier-Stokes equations with vacuum
• On the uniqueness of compressible fluid motions
• Remarks on the breakdown of smooth solutions for the 3-D Euler equations
• The initial value problem for the equations of motion of viscous and heat-conductive gases
• Factorization theorems for Hardy spaces in several variables
• Best constant in Sobolev inequality
• Unique global solution with respect to time of initial-boundary value problems for one-dimensional equations of a viscous gas
• Regularity results for two-dimensional flows of multiphase viscous fluids
• Unique solvability of the initial boundary value problems for compressible viscous fluids.
• Global existence in critical spaces for compressible Navier-Stokes equations
• 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
• Compensated compactness and Hardy spaces
• On existence of global solutions to the two-dimensional Navier-Stokes equations for a compressible viscous fluid
• Global well-posedness of 2D compressible Navier-Stokes equations with large data and vacuum
• Compressible Flows with a Density-Dependent Viscosity Coefficient
• Serrin-Type Criterion for the Three-Dimensional Viscous Compressible Flows
• 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
• A note on limiting cases of sobolev embeddings and convolution inequalities
• On Commutators of Singular Integrals and Bilinear Singular Integrals
• On the Global Existence of Weak Solutions for the Navier–Stokes Equations of Compressible Fluid Flows
• Characterizations of bounded mean oscillation
• Le problème de Cauchy pour les équations différentielles d'un fluide général
• On the existence of globally defined weak solutions to the Navier-Stokes equations