On some inequalities for solutions of equations describing the motion of a viscous compressible heat-conducting capillary fluid bounded by a free surface

Volume 28 / 2001

Ewa Zadrzy/nska, Wojciech M. Zaj/aczkowski Applicationes Mathematicae 28 (2001), 31-53 MSC: 35Q35, 35R35, 76N10. DOI: 10.4064/am28-1-3

Abstract

We derive inequalities for a local solution of a free boundary problem for a viscous compressible heat-conducting capillary fluid. The inequalities are crucial in proving the global existence of solutions belonging to certain anisotropic Sobolev–Slobodetskii space and close to an equilibrium state.

Authors

  • Ewa Zadrzy/nskaInstitute of Mathematics
    Polish Academy of Sciences
    /Sniadeckich 8
    00-950 Warszawa, Poland
    and
    Department of Mathematics and Information Science
    Warsaw University of Technology
    Plac Politechniki 1
    00-661 Warszawa, Poland
    e-mail
  • Wojciech M. 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
    00-908 Warszawa, Poland
    e-mail

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