Global weak solvability to the regularized viscous compressible heat conductive flow

Jiří Neustupa; Antonín Novotný

Applications of Mathematics (1991)

  • Volume: 36, Issue: 6, page 417-431
  • ISSN: 0862-7940

Abstract

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The concept of regularization to the complete system of Navier-Stokes equations for viscous compressible heat conductive fluid is developed. The existence of weak solutions for the initial boundary value problem for the modified equations is proved. Some energy and etropy estimates independent of the parameter of regularization are derived.

How to cite

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Neustupa, Jiří, and Novotný, Antonín. "Global weak solvability to the regularized viscous compressible heat conductive flow." Applications of Mathematics 36.6 (1991): 417-431. <http://eudml.org/doc/15690>.

@article{Neustupa1991,
abstract = {The concept of regularization to the complete system of Navier-Stokes equations for viscous compressible heat conductive fluid is developed. The existence of weak solutions for the initial boundary value problem for the modified equations is proved. Some energy and etropy estimates independent of the parameter of regularization are derived.},
author = {Neustupa, Jiří, Novotný, Antonín},
journal = {Applications of Mathematics},
keywords = {compressible heat conductive fluid; global existence; initial or boundary value problems; energ inequality; regularization; Navier-Stokes equations; weak solutions; energy and entropy estimates; global existence; regularization; Navier-Stokes equations; compressible heat conductive fluid; weak solutions; energy and entropy estimates},
language = {eng},
number = {6},
pages = {417-431},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global weak solvability to the regularized viscous compressible heat conductive flow},
url = {http://eudml.org/doc/15690},
volume = {36},
year = {1991},
}

TY - JOUR
AU - Neustupa, Jiří
AU - Novotný, Antonín
TI - Global weak solvability to the regularized viscous compressible heat conductive flow
JO - Applications of Mathematics
PY - 1991
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 36
IS - 6
SP - 417
EP - 431
AB - The concept of regularization to the complete system of Navier-Stokes equations for viscous compressible heat conductive fluid is developed. The existence of weak solutions for the initial boundary value problem for the modified equations is proved. Some energy and etropy estimates independent of the parameter of regularization are derived.
LA - eng
KW - compressible heat conductive fluid; global existence; initial or boundary value problems; energ inequality; regularization; Navier-Stokes equations; weak solutions; energy and entropy estimates; global existence; regularization; Navier-Stokes equations; compressible heat conductive fluid; weak solutions; energy and entropy estimates
UR - http://eudml.org/doc/15690
ER -

References

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  1. S. Agmon A. Douglis L. Nirenberg, 10.1002/cpa.3160170104, Comm. Pure Appl. Math. 17 (1964), 35-92. (1964) MR0162050DOI10.1002/cpa.3160170104
  2. A. Friedman, Partial differential equations of parabolic type, Prentice-Hall, INC (1964). (1964) Zbl0144.34903MR0181836
  3. A. Kufner O. John S. Fučík, Function spaces, Praha, Academia (1977). (1977) MR0482102
  4. O. A. Ladzhenskaya V. A. Solonnikov N. N. Uralceva, Linear and quasilinear equations of parabolic type, (Russian). Moskva, Nauka (1967). (1967) 
  5. J. L. Lions, Quelques méthodes des résolution des problèmes aux limites non linéaires, Dunod, Paris (1969). (1969) MR0259693
  6. A. Matsumura T. Nishida, 10.1007/BF01214738, Comm. Math. Phys. 89 (1983), 445 - 464. (1983) MR0713680DOI10.1007/BF01214738
  7. A. Matsumura T. Nishida, 10.1215/kjm/1250522322, J. Math. Kyoto Univ. 20 (1980), 67-104. (1980) MR0564670DOI10.1215/kjm/1250522322
  8. S. Mizohata, Theory of partial differential equations, (Russian). Moskva, Mir (1977). (1977) 
  9. J. Nečas A. Novotný M. Šilhavý, Global solution to the compressible isothermal multipolar fluid, to appear J. Math. Anal. Appl. (1991). (1991) MR1135273
  10. J. Nečas M. Šilhavý, Multipolar viscous fluids, to appear Quart. Appl. Math. MR1106391
  11. J. Neustupa, The global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid, Apl. Mat. 33 (1988), 389-409. (1988) MR0961316
  12. J. Neustupa A. Novotný, Uniqueness to the regularized viscous compressible heat conductive flow, to appear. 
  13. M. Padula, 10.1016/0022-1236(86)90108-4, J. Funct. Anal. 69 (1986), 1-20. (1986) MR0864756DOI10.1016/0022-1236(86)90108-4
  14. R. Rautman, 10.1007/BFb0087652, Lecture Notes in Math. Vol. 561, Springer-Verlag (1976). (1976) MR0463727DOI10.1007/BFb0087652
  15. A. Tani, 10.2977/prims/1195190106, Publ. RIMS Kyoto Univ. 13 (1977), 193 - 253. (1977) Zbl0366.35070DOI10.2977/prims/1195190106
  16. R. Temam, Navier-Stokes equations, Amsterdam-New York-Oxford (1979). (1979) Zbl0454.35073
  17. A. Valli, 10.1007/BF01761495, Ann. Mat. Рurа Appl. 130 (1982), 197-213. (1982) Zbl0599.76082MR0663971DOI10.1007/BF01761495

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