| Title:
|
Global weak solvability to the regularized viscous compressible heat conductive flow (English) |
| Author:
|
Neustupa, Jiří |
| Author:
|
Novotný, Antonín |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
36 |
| Issue:
|
6 |
| Year:
|
1991 |
| Pages:
|
417-431 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
compressible heat conductive fluid |
| Keyword:
|
global existence |
| Keyword:
|
initial or boundary value problems |
| Keyword:
|
energ inequality |
| Keyword:
|
regularization |
| Keyword:
|
Navier-Stokes equations |
| Keyword:
|
weak solutions |
| Keyword:
|
energy and entropy estimates |
| MSC:
|
35Q30 |
| MSC:
|
76N10 |
| idZBL:
|
Zbl 0742.76063 |
| idMR:
|
MR1134919 |
| DOI:
|
10.21136/AM.1991.104479 |
| . |
| Date available:
|
2008-05-20T18:42:31Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/104479 |
| . |
| Reference:
|
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| Reference:
|
[2] A. Friedman: Partial differential equations of parabolic type.Prentice-Hall, INC (1964). Zbl 0144.34903, MR 0181836 |
| Reference:
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[3] A. Kufner O. John S. Fučík: Function spaces.Praha, Academia (1977). MR 0482102 |
| Reference:
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[4] O. A. Ladzhenskaya V. A. Solonnikov N. N. Uralceva: Linear and quasilinear equations of parabolic type.(Russian). Moskva, Nauka (1967). |
| Reference:
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[5] J. L. Lions: Quelques méthodes des résolution des problèmes aux limites non linéaires.Dunod, Paris (1969). MR 0259693 |
| Reference:
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[6] A. Matsumura T. Nishida: Initial boundary value problems for the equation of motion of compressible viscous and heat conductive fluids.Comm. Math. Phys. 89 (1983), 445 - 464. MR 0713680, 10.1007/BF01214738 |
| Reference:
|
[7] A. Matsumura T. Nishida: The initial value problem for the equations of motion of viscous and heat conductive gasses.J. Math. Kyoto Univ. 20 (1980), 67-104. MR 0564670, 10.1215/kjm/1250522322 |
| Reference:
|
[8] S. Mizohata: Theory of partial differential equations.(Russian). Moskva, Mir (1977). |
| Reference:
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[9] J. Nečas A. Novotný M. Šilhavý: Global solution to the compressible isothermal multipolar fluid.to appear J. Math. Anal. Appl. (1991). MR 1135273 |
| Reference:
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[10] J. Nečas M. Šilhavý: Multipolar viscous fluids.to appear Quart. Appl. Math. MR 1106391 |
| Reference:
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[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. MR 0961316 |
| Reference:
|
[12] J. Neustupa A. Novotný: Uniqueness to the regularized viscous compressible heat conductive flow.to appear. |
| Reference:
|
[13] M. Padula: Existence of global solutions for 2-dimensional viscous compressible flow.J. Funct. Anal. 69 (1986), 1-20. MR 0864756, 10.1016/0022-1236(86)90108-4 |
| Reference:
|
[14] R. Rautman: The uniqueness and regularity of the solutions of Navier-Stokes problems.Lecture Notes in Math. Vol. 561, Springer-Verlag (1976). MR 0463727, 10.1007/BFb0087652 |
| Reference:
|
[15] A. Tani: On the first initial boundary value problem of compressible viscous fluid.Publ. RIMS Kyoto Univ. 13 (1977), 193 - 253. Zbl 0366.35070, 10.2977/prims/1195190106 |
| Reference:
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[16] R. Temam: Navier-Stokes equations.Amsterdam-New York-Oxford (1979). Zbl 0454.35073 |
| Reference:
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| . |
