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Low stratification of the complete Euler system

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Abstract

The present paper takes advantage of the concept of dissipative measure-valued solutions to show the rigorous derivation of the Euler–Boussinesq (EB) system that has been successfully used in various meteorological models. In particular, we show that EB system can be obtained as a singular limit of the complete Euler system. We provide two types of result—firstly, we treat the case of well-prepared initial data for any sufficiently regular bounded domain. Secondly, we use the dispersive estimates for acoustic equation to tackle the case of the ill-prepared initial data on an unbounded exterior domain.

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Authors and Affiliations

  1. Kyushu University, 744 Motooka, Nishi-ku, Fukuoka, 819-0395, Japan

    Jan Březina

  2. Institute of Mathematics CAS, Žitná 25, 115 67, Praha 1, Czechia

    Václav Mácha

Authors
  1. Jan Březina
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  2. Václav Mácha
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Correspondence to Václav Mácha.

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The work of Václav Mácha was supported by the Czech Science Foundation Project No. GA18-05974S in the framework of RVO: 67985840.

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Březina, J., Mácha, V. Low stratification of the complete Euler system. J. Evol. Equ. 21, 735–761 (2021). https://doi.org/10.1007/s00028-020-00599-6

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  • DOI: https://doi.org/10.1007/s00028-020-00599-6

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