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

Aplikace matematiky (1988)

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

## Access Full Article

top## Abstract

top## How to cite

topNeustupa, 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

top- O. A. Ladyzhenskaya N. N. Uralceva, Linear and Quasilinear Equations of the Elliptic Type, Nauka, Moscow, 1973 (Russian). (1973) MR0509265
- L. G. Loicianskij, Mechanics of Liquids and Gases, Nauka, Moscow, 1973 (Russian). (1973)
- A. Matsumura T. Nishida, 10.1215/kjm/1250522322, J. Math. Kyoto Univ. 20 (1980), 67-104, (1980) MR0564670DOI10.1215/kjm/1250522322
- J. Neustupa, A Note to the Global Weak Solvability of the Navier-Stokes Equations for Compressible Fluid, to appear prob. in Apl. mat. MR0961316
- 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
- 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
- R. Temam, Navier-Stokes Equations, North-Holland Publishing Company, Amsterdam- New York-Oxford, 1977. (1977) Zbl0383.35057MR0769654
- A. Valli, 10.1007/BF01761495, Ann. Mat. Рurа Appl. 130 (1982), 197-213. (1982) Zbl0599.76082MR0663971DOI10.1007/BF01761495
- 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

## Citations in EuDML Documents

top## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.