Formation of singularity and smooth wave propagation for the non-isentropic compressible Euler equations

Details Formation of singularity and smooth wave propagation for the non-isentropic compressible Euler equations Formation of singularity and smooth wave propagation for the non-isentropic compressible Euler equations

2011-05-02

arxiv.org/abs/1105.0231v1

Mathematics

Analysis of PDEs

to appear in J. Hyperbolic Diff. Eqs

Scientific paper

We define compressive and rarefactive waves and give the differential equations describing smooth wave steepening for the compressible Euler equations with a varying entropy profile and general pressure laws. Using these differential equations, we directly generalize P. Lax's singularity (shock) formation results for hyperbolic systems with two variables to the compressible Euler equations for a polytropic ideal gas. Our results are valid globally without restriction on the size of the variation of initial data.

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