Global existence of solutions to resonant system of isentropic gas dynamics

DOI10.1016/j.nonrwa.2011.04.005zbMath1230.35104OpenAlexW2022280001MaRDI QIDQ635243

Yun-Guang Lu

Publication date: 19 August 2011

Published in: Nonlinear Analysis. Real World Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.nonrwa.2011.04.005

zbMATH Keywords

maximum principleglobal solutionflux approximationcompensated compactness methodnonhomogeneous system of gas dynamics

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) First-order nonlinear hyperbolic equations (35L60) Initial value problems for first-order hyperbolic systems (35L45) Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics (76N10)

Related Items (20)

Zero relaxation time limits to a hydrodynamic model of two carrier types for semiconductors ⋮ Existence of a global solution for a scalar conservation law with a source term, nonlinear resonance, invariant region depending on the space variable ⋮ Cauchy problem for isothermal system in a general nozzle with space-dependent friction ⋮ Global solutions to isothermal system in a divergent nozzle with friction ⋮ Global \(L^\infty\) solutions to system of isentropic gas dynamics in a divergent nozzle with friction ⋮ Global entropy solutions to the compressible Euler equations in the isentropic nozzle flow for large data. Application of the generalized invariant regions and the modified Godunov scheme ⋮ Global existence of solutions to system of polytropic gas dynamics with friction ⋮ Isentropic gas flow for the compressible Euler equation in a nozzle ⋮ Global solutions of the Cauchy problem to Euler-Poisson equations of two-carrier types ⋮ On the compressible Euler dynamics equations in transonic flow ⋮ Existence of entropy solutions to system of polytropic gas with a class of unbounded sources ⋮ Global solutions and relaxation limit to the Cauchy problem of a hydrodynamic model for semiconductors ⋮ The global existence of L∞$L^{\infty }$ solutions to isentropic Euler equations in general nozzle ⋮ Global existence of solutions for a nonstrictly hyperbolic system ⋮ Existence of global solutions for isentropic gas flow with friction ⋮ Existence of a global solution to a scalar conservation law with a source term for large data ⋮ Existence of global solutions for isentropic gas flow in a divergent nozzle with friction ⋮ Global existence and stability to the polytropic gas dynamics with an outer force ⋮ Spherically symmetric solutions of the full compressible Euler equations in \(\mathbb R^N\) ⋮ Existencia global y estabilidad para un sistema de dinámica de gases isotérmico con una fuerza externa

Cites Work

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• Convergence of the fractional step Lax-Friedrichs scheme and Godunov scheme for the isentropic system of gas dynamics
• Convergence of the viscosity method for isentropic gas dynamics
• A generalized Riemann problem for quasi-one-dimensional gas flows
• Nonlinear stability and instability of transonic flows through a nozzle
• Quasilinear hyperbolic systems
• Kinetic formulation of the isentropic gas dynamics and \(p\)-systems
• Existence of solutions to hyperbolic conservation laws with a source
• Existence theory for the isentropic Euler equations
• The compressible Euler equations for an isothermal gas with spherical symmetry
• Global solutions to the compressible Euler equations with geometrical structure
• Some results for general systems of isentropic gas dynamics
• Global \(L^{\infty}\) solutions of the compressible Euler equations with spherical symmetry
• Multiple Steady States for 1-D Transonic Flow
• Nonlinear resonance for quasilinear hyperbolic equation
• Nonlinear Resonance in Systems of Conservation Laws
• Solutions in the large for nonlinear hyperbolic systems of equations

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