Incompressible limit for the two-dimensional isentropic Euler system with critical initial data

Taoufik Hmidi; Samira Sulaiman

doi:10.1017/S0308210512000509

Incompressible limit for the two-dimensional isentropic Euler system with critical initial data

Taoufik Hmidi, Samira Sulaiman

Mathematics

Research output: Contribution to journal › Article › peer-review

Abstract

We study the low-Mach-number limit for the two-dimensional isentropic Euler system with ill-prepared initial data belonging to the critical Besov space. By combining Strichartz estimates with the special structure of the vorticity, we prove that the lifespan of the solutions goes to infinity as the Mach number goes to zero. We also prove strong convergence results of the incompressible parts to the solution of the incompressible Euler system.

Original language	English (US)
Pages (from-to)	1127-1154
Number of pages	28
Journal	Proceedings of the Royal Society of Edinburgh Section A: Mathematics
Volume	144
Issue number	6
DOIs	https://doi.org/10.1017/S0308210512000509
State	Published - Dec 1 2014

ASJC Scopus subject areas

General Mathematics

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abstract = "We study the low-Mach-number limit for the two-dimensional isentropic Euler system with ill-prepared initial data belonging to the critical Besov space. By combining Strichartz estimates with the special structure of the vorticity, we prove that the lifespan of the solutions goes to infinity as the Mach number goes to zero. We also prove strong convergence results of the incompressible parts to the solution of the incompressible Euler system.",

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Incompressible limit for the two-dimensional isentropic Euler system with critical initial data

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