On the vacuum state for the equations of isentropic gas dynamics

DOI10.1016/0022-247X(87)90253-8zbMath0644.76084OpenAlexW2044228622MaRDI QIDQ1102809

Longwei Lin

Publication date: 1987

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0022-247x(87)90253-8

Mathematics Subject Classification ID

Related Items (36)

Singular behavior of vacuum states for compressible fluids ⋮ Local well-posedness of the three dimensional compressible Euler-Poisson equations with physical vacuum ⋮ Development of singularities in the relativistic Euler equations ⋮ Singularity Formation for the Compressible Euler Equations ⋮ Open Questions in the Theory of One Dimensional Hyperbolic Conservation Laws ⋮ Convergence of The Lax–Friedrichs' Scheme For Equaitons of Isentropic Gas Dynamics in Lagrangian Coordinates^∗ ⋮ Vacuum states and equidistribution of the random sequence for Glimm's scheme ⋮ Existence of globally bounded continuous solutions for nonisentropic gas dynamics equations ⋮ Formation of singularities for the relativistic Euler equations ⋮ Characteristics Method in a Certain Macroscopic Sense for Glimm'Scheme^∗ ⋮ Eulerian droplet model: delta-shock waves and solution of the Riemann problem ⋮ Well-posedness for the motion of physical vacuum of the three-dimensional compressible Euler equations with or without self-gravitation ⋮ Some results on Newtonian gaseous stars -- existence and stability ⋮ On exact solutions of rarefaction-rarefaction interactions in compressible isentropic flow ⋮ Well-posedness in smooth function spaces for the moving-boundary three-dimensional compressible Euler equations in physical vacuum ⋮ Absence of singularities in solutions for the compressible Euler equations with source terms in ⋮ Singularity Formation for Radially Symmetric Expanding Wave of Compressible Euler Equations ⋮ Well-posedness and blow-up criterion for the Chaplygin gas equations in ℝN ⋮ On the blow-up phenomena of solutions for the full compressible Euler equations in ${{\mathbb{R}}^{N}}$ ⋮ Composite wave interactions and the collapse of vacuums in gas dynamics ⋮ Singularities in finite time of the full compressible Euler equations in \(\mathbb{R}^d\) ⋮ Lack of BV bounds for approximate solutions to the \(p\)-system with large data ⋮ Global smooth solution of the nonisentropic gas dynamics system ⋮ Global smooth solutions for the Chaplygin gas equations with source terms in \(\mathbb{R}^d\) ⋮ Local existence with physical vacuum boundary condition to Euler equations with damping ⋮ A priori estimates for the free-boundary 3D compressible Euler equations in physical vacuum ⋮ Isentropic approximation and Gevrey regularity for the full compressible Euler equations in \(\mathbb{R}^N\) ⋮ Optimal density lower bound on nonisentropic gas dynamics ⋮ Weak solutions for an inviscid two-phase flow model in physical vacuum ⋮ Qualitative analysis of solution for the full compressible Euler equations in RN ⋮ Well-posedness in smooth function spaces for moving-boundary 1-D compressible euler equations in physical vacuum ⋮ A priori estimates for solutions to the relativistic Euler equations with a moving vacuum boundary ⋮ Global existence of near-affine solutions to the compressible Euler equations ⋮ Well-posedness of non-isentropic Euler equations with physical vacuum ⋮ Finite Time Singularities for Hyperbolic Systems ⋮ On vanishing pressure limit of continuous solutions to the isentropic Euler equations

Cites Work

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• Unnamed Item
• A constructive theory for shock-free, isentropic flow
• On the vacuum state for the isentropic gas dynamics equations
• Global existence of solutions to nonlinear hyperbolic systems of conservation laws
• Polygonal approximations of solutions of the initial value problem for a conservation law
• Development of Singularities of Solutions of Nonlinear Hyperbolic Partial Differential Equations
• Solutions in the large for nonlinear hyperbolic systems of equations
• Global continuous solutions of hyperbolic systems of quasi-linear equations

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