Incompressible limit of Euler equations with damping

Fei Shi; Fei Shi

doi:10.3934/era.2022007

Electronic Research Archive

2022, Volume 30, Issue 1: 126-139. doi: 10.3934/era.2022007

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Research article

Incompressible limit of Euler equations with damping

Fei Shi ^,

Department of Mathematics, Institute of Systems Biology, Shanghai University, Shanghai, China

Received: 12 September 2021 Revised: 02 October 2021 Accepted: 09 October 2021 Published: 13 December 2021

The Cauchy problem for the compressible Euler system with damping is considered in this paper. Based on previous global existence results, we further study the low Mach number limit of the system. By constructing the uniform estimates of the solutions in the well-prepared initial data case, we are able to prove the global convergence of the solutions in the framework of small solutions.
- incompressible limit,
- Mach number,
- Euler equations,
- damping,
- global solution
Citation: Fei Shi. Incompressible limit of Euler equations with damping[J]. Electronic Research Archive, 2022, 30(1): 126-139. doi: 10.3934/era.2022007

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Abstract

The Cauchy problem for the compressible Euler system with damping is considered in this paper. Based on previous global existence results, we further study the low Mach number limit of the system. By constructing the uniform estimates of the solutions in the well-prepared initial data case, we are able to prove the global convergence of the solutions in the framework of small solutions.

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