A remark on the smoothness of bounded regions filled with a steady compressible and isentropic fluid

Sébastien Novo; Antonín Novotný

Applications of Mathematics (2005)

  • Volume: 50, Issue: 4, page 331-339
  • ISSN: 0862-7940

Abstract

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For convenient adiabatic constants, existence of weak solutions to the steady compressible Navier-Stokes equations in isentropic regime in smooth bounded domains is well known. Here we present a way how to prove the same result when the bounded domains considered are Lipschitz.

How to cite

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Novo, Sébastien, and Novotný, Antonín. "A remark on the smoothness of bounded regions filled with a steady compressible and isentropic fluid." Applications of Mathematics 50.4 (2005): 331-339. <http://eudml.org/doc/33225>.

@article{Novo2005,
abstract = {For convenient adiabatic constants, existence of weak solutions to the steady compressible Navier-Stokes equations in isentropic regime in smooth bounded domains is well known. Here we present a way how to prove the same result when the bounded domains considered are Lipschitz.},
author = {Novo, Sébastien, Novotný, Antonín},
journal = {Applications of Mathematics},
keywords = {Navier-Stokes equations; compressible fluid; weak solution; Navier-Stokes equations; compressible fluid; weak solution},
language = {eng},
number = {4},
pages = {331-339},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A remark on the smoothness of bounded regions filled with a steady compressible and isentropic fluid},
url = {http://eudml.org/doc/33225},
volume = {50},
year = {2005},
}

TY - JOUR
AU - Novo, Sébastien
AU - Novotný, Antonín
TI - A remark on the smoothness of bounded regions filled with a steady compressible and isentropic fluid
JO - Applications of Mathematics
PY - 2005
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 50
IS - 4
SP - 331
EP - 339
AB - For convenient adiabatic constants, existence of weak solutions to the steady compressible Navier-Stokes equations in isentropic regime in smooth bounded domains is well known. Here we present a way how to prove the same result when the bounded domains considered are Lipschitz.
LA - eng
KW - Navier-Stokes equations; compressible fluid; weak solution; Navier-Stokes equations; compressible fluid; weak solution
UR - http://eudml.org/doc/33225
ER -

References

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  1. The solution of some problems of vector analysis, associated with the operators div and grad, Trudy Semin. S. L.  Soboleva 1 (1980), 5–40. (Russian) (1980) MR0631691
  2. 10.1007/BF01393835, Invent. Math. 98 (1989), 511–547. (1989) MR1022305DOI10.1007/BF01393835
  3. Measure Theory and Fine Properties of Functions. Studies in Advanced Mathematics, CRC Press, Boca Raton, 1992. (1992) MR1158660
  4. Mathematical Topics in Fluid Mechanics, Vol.  2. Compressible Models. Lecture Series in Mathematics and its Applications, Clarendon Press, Oxford, 1998. (1998) MR1637634
  5. 10.1215/kjm/1250283849, J.  Math. Kyoto Univ. 42 (2002), 531–550. (2002) MR1967222DOI10.1215/kjm/1250283849
  6. On the existence of weak solutions to the steady compressible Navier-Stokes equations in domains with conical outlets, J. Math. Fluid Mech. 7 (2005), 1–24. (2005) MR2220444

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