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Incompressible Limits and Propagation of Acoustic Waves in Large Domains with Boundaries

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Abstract

We study the incompressible limit for the full Navier-Stokes-Fourier system on unbounded domains with boundaries, supplemented with the complete slip boundary condition for the velocity field. Using an abstract result of Tosio Kato we show that the energy of acoustic waves decays to zero on any compact subset of the physical space. This in turn implies strong convergence of the velocity field to its limit in the incompressible regime.

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Authors and Affiliations

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

    Eduard Feireisl

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  1. Eduard Feireisl
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Correspondence to Eduard Feireisl.

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Communicated by P. Constantin

The work of E.F. was supported by Grant 201/08/0315 of GA ČR as a part of the general research programme of the Academy of Sciences of the Czech Republic, Institutional Research Plan AV0Z10190503.

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Feireisl, E. Incompressible Limits and Propagation of Acoustic Waves in Large Domains with Boundaries. Commun. Math. Phys. 294, 73–95 (2010). https://doi.org/10.1007/s00220-009-0954-6

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