Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid

Jiří Neustupa

Aplikace matematiky (1988)

  • Volume: 33, Issue: 5, page 389-409
  • ISSN: 0862-7940

Abstract

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The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally, a so called energy inequality is derived. The inequality is independent on the regularization used.

How to cite

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Neustupa, Jiří. "Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid." Aplikace matematiky 33.5 (1988): 389-409. <http://eudml.org/doc/15552>.

@article{Neustupa1988,
abstract = {The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally, a so called energy inequality is derived. The inequality is independent on the regularization used.},
author = {Neustupa, Jiří},
journal = {Aplikace matematiky},
keywords = {Navier-Stoke equations; method of a discretization in time; global existence of weak solutions; mixed initial-boundary value problem; viscous compressible fluid; Navier-Stoke equations; method of a discretization in time; global existence of weak solutions; mixed initial-boundary value problem; viscous compressible fluid},
language = {eng},
number = {5},
pages = {389-409},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid},
url = {http://eudml.org/doc/15552},
volume = {33},
year = {1988},
}

TY - JOUR
AU - Neustupa, Jiří
TI - Global weak solvability of a regularized system of the Navier-Stokes equations for compressible fluid
JO - Aplikace matematiky
PY - 1988
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 33
IS - 5
SP - 389
EP - 409
AB - The paper contains the proof of global existence of weak solutions to the mixed initial-boundary value problem for a certain modification of a system of equations of motion of viscous compressible fluid. The modification is based on an application of an operator of regularization to some terms appearing in the system of equations and it does not contradict the laws of fluid mechanics. It is assumed that pressure is a known function of density. The method of discretization in time is used and finally, a so called energy inequality is derived. The inequality is independent on the regularization used.
LA - eng
KW - Navier-Stoke equations; method of a discretization in time; global existence of weak solutions; mixed initial-boundary value problem; viscous compressible fluid; Navier-Stoke equations; method of a discretization in time; global existence of weak solutions; mixed initial-boundary value problem; viscous compressible fluid
UR - http://eudml.org/doc/15552
ER -

References

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  1. O. A. Ladyzhenskaya N. N. Uralceva, Linear and Quasilinear Equations of the Elliptic Type, Nauka, Moscow, 1973 (Russian). (1973) MR0509265
  2. L. G. Loicianskij, Mechanics of Liquids and Gases, Nauka, Moscow, 1973 (Russian). (1973) 
  3. A. Matsumura T. Nishida, 10.1215/kjm/1250522322, J. Math. Kyoto Univ. 20 (1980), 67-104, (1980) MR0564670DOI10.1215/kjm/1250522322
  4. J. Neustupa, A Note to the Global Weak Solvability of the Navier-Stokes Equations for Compressible Fluid, to appear prob. in Apl. mat. MR0961316
  5. R. Rautmann, The Uniqueness and Regularity of the Solutions of Navier-Stokes Problems, Functional Theoretic Methods for Partial Differential Equations, Proc. conf. Darmstadt 1976, Lecture Notes in Mathematics, Vol. 561, Berlin-Heidelberg-New York, Springer-Verlag, 1976, 378-393. (1976) Zbl0383.35059MR0463727
  6. V. A. Sollonikov, 10.1007/BF01562053, J. Soviet Math. 14 (1980), 1120-1133 (previously in Zap. Nauchn. Sem. LOMI 56 (1976), 128-142 (Russian)). (1980) MR0481666DOI10.1007/BF01562053
  7. R. Temam, Navier-Stokes Equations, North-Holland Publishing Company, Amsterdam- New York-Oxford, 1977. (1977) Zbl0383.35057MR0769654
  8. A. Valli, 10.1007/BF01761495, Ann. Mat. Рurа Appl. 130 (1982), 197-213. (1982) Zbl0599.76082MR0663971DOI10.1007/BF01761495
  9. A. Valli, Periodic and Stationary Solutions for Compressible Navier-Stokes Equations via a Stability Method, Ann. Scuola Norm. Sup. Pisa, (IV) 10 (1983), 607-647. (1983) Zbl0542.35062MR0753158

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