| Title:
|
Additional note on partial regularity of weak solutions of the Navier-Stokes equations in the class $L^\infty (0,T,L^3(\Omega )^3)$ (English) |
| Author:
|
Skalák, Zdeněk |
| Language:
|
English |
| Journal:
|
Applications of Mathematics |
| ISSN:
|
0862-7940 (print) |
| ISSN:
|
1572-9109 (online) |
| Volume:
|
48 |
| Issue:
|
2 |
| Year:
|
2003 |
| Pages:
|
153-159 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We present a simplified proof of a theorem proved recently concerning the number of singular points of weak solutions to the Navier-Stokes equations. If a weak solution ${\mathbf u}$ belongs to $L^\infty (0,T,L^3(\Omega )^3)$, then the set of all possible singular points of ${\mathbf u}$ in $\Omega $ is at most finite at every time $t_0\in (0,T)$. (English) |
| Keyword:
|
Navier-Stokes equations |
| Keyword:
|
partial regularity |
| MSC:
|
35B65 |
| MSC:
|
35D10 |
| MSC:
|
35Q10 |
| MSC:
|
35Q30 |
| MSC:
|
76D03 |
| MSC:
|
76D05 |
| idZBL:
|
Zbl 1099.35089 |
| idMR:
|
MR1966346 |
| DOI:
|
10.1023/A:1026046211510 |
| . |
| Date available:
|
2009-09-22T18:13:05Z |
| Last updated:
|
2020-07-02 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134524 |
| . |
| 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] H. Kozono: Uniqueness and regularity of weak solutions to the Navier-Stokes equations.Lecture Notes Numer. Appl. Anal. 16 (1998), 161–208. Zbl 0941.35065, MR 1616331 |
| Reference:
|
[3] H. Kozono, H. Sohr: Remark on uniqueness of weak solutions to the Navier-Stokes equations.Analysis 16 (1996), 255–271. MR 1403221, 10.1524/anly.1996.16.3.255 |
| Reference:
|
[4] J. Neustupa: Partial regularity of weak solutions to the Navier-Stokes equations in the class $L^\infty (0,T,L^3(\Omega )^3)$.J. Math. Fluid Mech. 1 (1999), 309–325. MR 1738173, 10.1007/s000210050013 |
| Reference:
|
[5] Y. Taniuchi: On generalized energy inequality of the Navier-Stokes equations.Manuscripta Math. 94 (1997), 365–384. MR 1485443, 10.1007/BF02677860 |
| Reference:
|
[6] R. Temam: Navier-Stokes Equations.North-Holland, Amsterdam-New York-Oxford, 1977. Zbl 0383.35057, MR 0769654 |
| . |
