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On local-in-time existence for the Dirichlet problem for equations of compressible viscous fluids

Volume 78 / 2002

Piotr Boguslaw Mucha, Wojciech Zaj/aczkowski Annales Polonici Mathematici 78 (2002), 227-239 MSC: 35Q30, 76Q10. DOI: 10.4064/ap78-3-2

Abstract

The local existence of solutions for the compressible Navier–Stokes equations with the Dirichlet boundary conditions in the $L_p$-framework is proved. Next an almost-global-in-time existence of small solutions is shown. The considerations are made in Lagrangian coordinates. The result is sharp in the $L_p$-approach, because the velocity belongs to $W^{2,1}_r$ with $r>3$.

Authors

  • Piotr Boguslaw MuchaInstitute of Applied Mathematics and Mechanics
    Warsaw University
    Banacha 2
    02-097 Warszawa, Poland
    e-mail
  • Wojciech Zaj/aczkowskiInstitute of Mathematics
    Polish Academy of Sciences
    /Sniadeckich 8
    00-950 Warszawa, Poland
    and
    Institute of Mathematics
    and Operations Research
    Military University of Technology
    Kaliskiego 2
    01-489 Warszawa, Poland
    e-mail

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