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Inviscid Incompressible Limits Under Mild Stratification: A Rigorous Derivation of the Euler–Boussinesq System

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Abstract

We consider the full Navier–Stokes–Fourier system in the singular regime of small Mach and large Reynolds and Péclet numbers, with ill prepared initial data on an unbounded domain \(\Omega \subset R^3\) with a compact boundary. We perform the singular limit in the framework of weak solutions and identify the Euler–Boussinesq system as the target problem.

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Acknowledgments

The research of E. F. 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 work was supported by the MODTERCOM project within the APEX programme of the region Provence-Alpe-Côte d’Azur and by RVO: 67985840.

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Correspondence to Antonín Novotný.

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Feireisl, E., Novotný, A. Inviscid Incompressible Limits Under Mild Stratification: A Rigorous Derivation of the Euler–Boussinesq System. Appl Math Optim 70, 279–307 (2014). https://doi.org/10.1007/s00245-014-9243-7

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