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An anelastic approximation arising in astrophysics

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Abstract

We identify the asymptotic limit of the compressible non-isentropic Navier–Stokes system in the regime of low Mach, low Froude and high Reynolds number. The system is driven by a long range gravitational potential. We show convergence to an anelastic system for ill-prepared initial data. The proof is based on frequency localized Strichartz estimates for the acoustic equation based on the recent work of Metcalfe and Tataru.

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Authors and Affiliations

  1. Department of Information Engineering, Computer Science and Mathematics, University of L’Aquila, 67100, L’Aquila, Italy

    Donatella Donatelli

  2. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Eduard Feireisl

Authors
  1. Donatella Donatelli
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  2. Eduard Feireisl
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Corresponding author

Correspondence to Donatella Donatelli.

Additional information

The research of DD was partially supported by European Union MSCA-ITN-2014-ETN—Marie Sklodowska-Curie Innovative Training Networks (ITN-ETN) Project: Grant Agreement 642768 ModCompShock.

The research of EF leading to these results has received funding from the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007-2013)/ ERC Grant Agreement 320078. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840. EF thanks Gran Sasso Science Institute for hospitality and support during his stay in L’Aquila.

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Donatelli, D., Feireisl, E. An anelastic approximation arising in astrophysics. Math. Ann. 369, 1573–1597 (2017). https://doi.org/10.1007/s00208-016-1507-x

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  • DOI: https://doi.org/10.1007/s00208-016-1507-x

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