Existence of global smooth solution to the relativistic Euler equations

DOI10.1016/j.na.2004.09.019zbMath1072.35189OpenAlexW2037171229MaRDI QIDQ1764854

Changjiang Zhu, Lizhi Ruan

Publication date: 22 February 2005

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2004.09.019

zbMATH Keywords

maximum principleexistenceuniquenessCauchy problemMinkowski space-timeglobal smooth solution

Mathematics Subject Classification ID

Special relativity (83A05) PDEs in connection with relativity and gravitational theory (35Q75)

Related Items (15)

Development of singularities in the relativistic Euler equations ⋮ Sonic-supersonic solutions for the two dimensional steady relativistic Euler equations ⋮ Existence of periodic solutions to an isothermal relativistic Euler system ⋮ Formation of singularities for the relativistic Euler equations ⋮ Semi-hyperbolic patch characterized by 2D steady relativistic Euler equations ⋮ Special relativistic effects revealed in the Riemann problem for three-dimensional relativistic Euler equations ⋮ Two dimensional relativistic Euler equations in a convex duct ⋮ On the steady state relativistic Euler-Poisson equations ⋮ Local smooth solutions to the 3-dimensional isentropic relativistic Euler equations ⋮ Nonlinear hyperbolic waves in relativistic gases of massive particles with Synge energy ⋮ Global smooth solutions to relativistic Euler-Poisson equations with repulsive force ⋮ Limits of Riemann solutions to the relativistic Euler systems for Chaplygin gas as pressure vanishes ⋮ Non-relativistic global limits of entropy solutions to the extremely relativistic Euler equations ⋮ Sonic-supersonic solutions to a degenerate Cauchy-Goursat problem for 2D relativistic Euler equations ⋮ The special solutions of 2-D steady isentropic irrotational relativistic Euler system

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• Convergence to strong nonlinear diffusion waves for solutions of \(p\)-system with damping

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