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Waves in Flows pp 127–158Cite as

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Compressible Navier-Stokes System on a Moving Domain in the Lp − Lq Framework

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Abstract

We prove the local well-posedness for the barotropic compressible Navier-Stokes system on a moving domain, a motion of which is determined by a given vector field V, in a maximal L p − L q regularity framework. Under additional smallness assumptions on the data we show that our solution exists globally in time and satisfies a decay estimate. In particular, for the global well-posedness we do not require exponential decay or smallness of V in L p(L q). However, we require exponential decay and smallness of its derivatives.

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Authors and Affiliations

  1. Czech Academy of Sciences, Institute of Mathematics, Prague, Czech Republic

    Ondřej Kreml & Šárka Nečasová

  2. University of Warsaw, Institute of Applied Mathematics and Mechanics, Warszawa, Poland

    Tomasz Piasecki

Authors
  1. Ondřej Kreml
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  2. Šárka Nečasová
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  3. Tomasz Piasecki
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Correspondence to Ondřej Kreml .

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Editors and Affiliations

  1. Department of Technical Mathematics, Faculty of Mechanical Engineering, Czech Technical University, Prague, Czech Republic

    Tomáš Bodnár

  2. Department of Mechanical Engineering, University of Pittsburgh, Pittsburgh, PA, USA

    Giovanni P. Galdi

  3. Institute of Mathematics, Czech Academy of Sciences, Prague, Czech Republic

    Šárka Nečasová

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Kreml, O., Nečasová, Š., Piasecki, T. (2021). Compressible Navier-Stokes System on a Moving Domain in the Lp − Lq Framework. In: Bodnár, T., Galdi, G.P., Nečasová, Š. (eds) Waves in Flows. Advances in Mathematical Fluid Mechanics(). Birkhäuser, Cham. https://doi.org/10.1007/978-3-030-68144-9_5

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