Global existence of smooth solutions to two-dimensional compressible isentropic Euler equations for Chaplygin gases

DOI10.1007/s11425-010-0060-4zbMath1256.35084OpenAlexW1966594808MaRDI QIDQ973770

Yu-Zhu Wang, De-Xing Kong, Ke Feng Liu

Publication date: 26 May 2010

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

Full work available at URL: https://doi.org/10.1007/s11425-010-0060-4

zbMATH Keywords

Cauchy problemsmooth solutioncompressible Euler equationsirrotational flownull conditionChaplygin gases

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) First-order nonlinear hyperbolic equations (35L60) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

Related Items (20)

Completely linear degeneracy for quasilinear hyperbolic systems ⋮ Formation of singularities of solutions to the compressible Euler equations for a Chaplygin gas ⋮ Stabilizing effect of the power law inflation on isentropic relativistic fluids ⋮ Nonlinear instability for nonhomogeneous incompressible viscous fluids ⋮ Global classical solution to the three-dimensional isentropic compressible Navier-Stokes equations with general initial data ⋮ Singularity for the one-dimensional rotating Euler equations of Chaplygin gases ⋮ The lifespan of 3D radial solutions to the non-isentropic relativistic Euler equations ⋮ The Riemann problem for Chaplygin gas flow in a duct with discontinuous cross-section ⋮ The two-dimensional Riemann problem for Chaplygin gas dynamics with three constant states ⋮ The Riemann problem for one-dimensional generalized Chaplygin gas dynamics ⋮ Global and almost global existence for general quasilinear wave equations in two space dimensions ⋮ Asymptotic behavior of global classical solutions to Goursat problem for quasilinear hyperbolic systems with small BV data ⋮ The two dimensional gas expansion problem of the Euler equations for the generalized Chaplygin gas ⋮ Boundedness of the total energy of relativistic membranes evolving in a curved spacetime ⋮ Global radial solutions to 3D relativistic Euler equations for non-isentropic Chaplygin gases ⋮ The global smooth symmetric solution to 2-D full compressible Euler system of Chaplygin gases ⋮ Global smooth solutions to 3D irrotational Euler equations for Chaplygin gases ⋮ Global existence of smooth solutions to 2D Chaplygin gases on curved space ⋮ Global existence of smooth solution to relativistic membrane equation with large data ⋮ Global existence of classical solutions of Goursat problem for quasilinear hyperbolic systems with BV data

Cites Work

• Global existence of a class of smooth 3D spherically symmetric flows of Chaplygin gases with variable entropy
• Global solvability for systems of nonlinear wave equations with multiple speeds in two dimensions.
• Formation of singularities in three-dimensional compressible fluids
• Bäcklund transformations and their applications
• Supersonic flow and shock waves. Reprint of the ed. published by Interscience Publishers, New York
• The lifespan of a class of smooth spherically symmetric solutions of the compressible Euler equations with variable entropy in three space dimensions
• Delayed singularity formation in 2D compressible flow
• The Existence of Global Solutions to Systems of Quasilinear Wave Equations with Quadratic Nonlinearities in 2-Dimensional Space
• Global solutions of nonlinear hyperbolic equations for small initial data
• Uniform decay estimates and the lorentz invariance of the classical wave equation
• Long‐time behaviour of solutions of a system of nonlinear wave equations
• Remarks on the global sobolev inequalities in the minkowski space Rⁿ⁺¹
• Global smooth solutions to Euler equations for a perfect gas
• The null condition for quasilinear wave equations in two space dimensions. I
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