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On a Singular Limit for the Compressible Rotating Euler System

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Abstract

The work addresses a singular limit for a rotating compressible Euler system in the low Mach number and low Rossby number regime. Based on the concept of dissipative measure-valued solution, the quasi-geostrophic system is identified as the limit problem in the case of ill-prepared initial data. The ill-prepared initial data will cause rapidly oscillating acoustic waves. Using dispersive estimates of Strichartz type, the effect of the acoustic waves in the asymptotic limit is eliminated.

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Acknowledgements

The authors are grateful to the referee and the editor whose comments and suggestions greatly improved the presentation of this paper. The paper was written when Tong Tang was visiting the Institute of Mathematics of the Czech Academy of Sciences which hospitality and support is gladly acknowledged.

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Authors and Affiliations

  1. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 11567, Praha 1, Czech Republic

    Šárka Nečasová

  2. Department of Mathematics, College of Sciences, Hohai University, Nanjing, 210098, People’s Republic of China

    Tong Tang

Authors
  1. Šárka Nečasová
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  2. Tong Tang
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Correspondence to Šárka Nečasová.

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Communicated by M. Feistauer

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Šárka Nečasová: The research of Š.N. leading to these results has received funding from the Czech Sciences Foundation (GAČR), P201-16-032308 and RVO 67985840. Final version of the paper was made under support the Czech Sciences Foundation (GAČR), GA19-04243S. Tong Tang: The research of T.T. is supported by the NSFC Grant No. 11801138.

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Nečasová, Š., Tang, T. On a Singular Limit for the Compressible Rotating Euler System. J. Math. Fluid Mech. 22, 43 (2020). https://doi.org/10.1007/s00021-020-00504-8

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