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On the Domain Dependence of Solutions to the Compressible Navier-Stokes Equations of an Isothermal Fluid

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Abstract

The aim of this paper is to study the behaviour of the variational solutions to the Navier-Stokes equations describing viscous compressible isothermal fluids with nonlinear stress tensors in a sequence of domains \(\{\varOmega_{n}\} _{n=1}^{\infty}\). The sequence converges in sense of the Sobolev-Orlicz capacity to domain Ω. We prove that the solutions of the equations in Ω n converge to a solution of the respective equations in Ω. Moreover, The result can be applied to generalization of the existence result.

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Authors and Affiliations

  1. Mathematical Institute, Charles University, Prague, Czech Republic

    Nikola Hlaváčová

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  1. Nikola Hlaváčová
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Correspondence to Nikola Hlaváčová.

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The work was partly supported by the grant of the Czech Science Foundation No. 201/09/0917 and by the project LC06052 (Jindřich Nečas Center for Mathematical Modeling) and by the grant SVV-2011-263316.

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Hlaváčová, N. On the Domain Dependence of Solutions to the Compressible Navier-Stokes Equations of an Isothermal Fluid. Acta Appl Math 124, 187–206 (2013). https://doi.org/10.1007/s10440-012-9775-2

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  • DOI: https://doi.org/10.1007/s10440-012-9775-2

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