On weak-strong uniqueness and singular limit for the compressible Primitive Equations

Hongjun Gao; Šárka Nečasová; Tong Tang

doi:10.3934/dcds.2020181

Article Contents

2020, Volume 40, Issue 7: 4287-4305. Doi: 10.3934/dcds.2020181

This issue Previous Article Computability of topological entropy: From general systems to transformations on Cantor sets and the interval Next Article Local and global analyticity for $\mu$-Camassa-Holm equations

On weak-strong uniqueness and singular limit for the compressible Primitive Equations

1.
Jiangsu Provincial Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
2.
Key Laboratory of Ministry of Education for Virtual Geographic Environment, Jiangsu Center for Collaborative Innovation in Geographical, Information Resource Development and Application, Nanjing Normal University, Nanjing 210023, China
3.
Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 11567, Praha 1, Czech Republic
4.
Department of Mathematics, College of Sciences, Hohai University, Nanjing 210098, China

^* Corresponding author
^* Corresponding author

Received: June 2019

Revised: January 2020

Published: April 2020

The research of H. G is partially supported by the NSFC Grant No. 11531006. The research of Š.N. leading to these results has received funding from the Czech Sciences Foundation (GAČR), GA19-04243S and RVO 67985840. The research of T.T. is supported by the NSFC Grant No. 11801138.

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Abstract

The paper addresses the weak-strong uniqueness property and singular limit for the compressible Primitive Equations (PE). We show that a weak solution coincides with the strong solution emanating from the same initial data. On the other hand, we prove compressible PE will approach to the incompressible inviscid PE equations in the regime of low Mach number and large Reynolds number in the case of well-prepared initial data. To the best of the authors' knowledge, this is the first work to bridge the link between the compressible PE with incompressible inviscid PE.

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Mathematics Subject Classification: Primary: 35Q30.

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