| Title:
|
A note on the generalized energy inequality in the Navier-Stokes equations (English) |
| Author:
|
Kučera, Petr |
| Author:
|
Skalák, Zdeněk |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
48 |
| Issue:
|
6 |
| Year:
|
2003 |
| Pages:
|
537-545 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We prove that there exists a suitable weak solution of the Navier-Stokes equation, which satisfies the generalized energy inequality for every nonnegative test function. This improves the famous result on existence of a suitable weak solution which satisfies this inequality for smooth nonnegative test functions with compact support in the space-time. (English) |
| Keyword:
|
Navier-Stokes equations |
| Keyword:
|
suitable weak solution |
| Keyword:
|
generalized energy inequality |
| MSC:
|
35Q30 |
| MSC:
|
35Q35 |
| MSC:
|
76D03 |
| MSC:
|
76D05 |
| idZBL:
|
Zbl 1099.35099 |
| idMR:
|
MR2025962 |
| DOI:
|
10.1023/B:APOM.0000024492.23444.29 |
| . |
| Date available:
|
2009-09-22T18:15:50Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134549 |
| . |
| Reference:
|
[1] L. Caffarelli, R. Kohn and L. Nirenberg: Partial regularity of suitable weak solutions of the Navier-Stokes equations.Comm. Pure Appl. Math. 35 (1982), 771–831. MR 0673830, 10.1002/cpa.3160350604 |
| Reference:
|
[2] Y. Giga, H. Sohr: Abstract $L^p$ estimates for the Cauchy problem with applications to the Navier-Stokes equations in exterior domains.J. Funct. Anal. 102 (1991), 72–94. MR 1138838, 10.1016/0022-1236(91)90136-S |
| Reference:
|
[3] P. Kučera, Z. Skalák: Generalized energy inequality for suitable weak solutions of the Navier-Stokes equations.In: Proceedings of seminar Topical Problem of Fluid Mechanics 2003, Institute of Thermomechanics AS CR, J. Příhoda, K. Kozel (eds.), Prague, 2003, pp. 61–66. |
| Reference:
|
[4] A. Kufner, O. John, S. Fučík: Function Spaces.Academia, Prague, 1979. |
| Reference:
|
[5] J. Neustupa, A. Novotný, P. Penel: A remark to interior regularity of a suitable weak solution to the Navier-Stokes equations.Preprint, University of Toulon-Var, 1999. |
| Reference:
|
[6] G. A. Seregin: Local regularity of suitable weak solutions to the Navier-Stokes equations near the boundary.J. Math. Fluid Mech. 4 (2002), 1–29. Zbl 0997.35044, MR 1891072, 10.1007/s00021-002-8533-z |
| Reference:
|
[7] Z. Skalák, P. Kučera: Remark on regularity of weak solutions to the Navier-Stokes equations.Comment. Math. Univ. Carolin. 42 (2001), 111–117. MR 1825376 |
| Reference:
|
[8] R. Temam: Navier-Stokes Equations, Theory and Numerical Analysis.North-Holland Publishing Company, Amsterdam-New York-Oxford. Revised edition, 1979. Zbl 0426.35003, MR 0603444 |
| . |
