| Title:
|
Remark on regularity of weak solutions to the Navier-Stokes equations (English) |
| Author:
|
Skalák, Zdeněk |
| Author:
|
Kučera, Petr |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
42 |
| Issue:
|
1 |
| Year:
|
2001 |
| Pages:
|
111-117 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some results on regularity of weak solutions to the Navier-Stokes equations published recently in [3] follow easily from a classical theorem on compact operators. Further, weak solutions of the Navier-Stokes equations in the space $L^2(0,T,W^{1,3}(\varOmega)^3)$ are regular. (English) |
| Keyword:
|
Navier-Stokes equations |
| Keyword:
|
weak solution |
| Keyword:
|
regularity |
| MSC:
|
35D10 |
| MSC:
|
35Q10 |
| MSC:
|
35Q30 |
| MSC:
|
76D03 |
| MSC:
|
76D05 |
| MSC:
|
76F99 |
| idZBL:
|
Zbl 1038.35061 |
| idMR:
|
MR1825376 |
| . |
| Date available:
|
2009-01-08T19:08:42Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119227 |
| . |
| Reference:
|
[1] Giga Y.: Solutions for semilinear parabolic equations in $L^p$ and regularity of weak solutions of the Navier-Stokes system.J. Differential Equations 62 (1986), 182-212. MR 0833416 |
| Reference:
|
[2] Kato T.: Perturbation Theory for Linear Operators.Springer-Verlag, Berlin, Heidelberg, New York 1980. Zbl 0836.47009 |
| Reference:
|
[3] Kozono H.: Uniqueness and regularity of weak solutions to the Navier-Stokes equations.Lecture Notes in Num. and Appl. Anal. 16 (1998), 161-208. Zbl 0941.35065, MR 1616331 |
| Reference:
|
[4] Neustupa J.: Partial regularity of weak solutions to the Navier-Stokes Equations in the class $L^\infty(0,T,L^3(\varOmega))$.J. Math. Fluid Mech. 1 (1999), 1-17. MR 1738173 |
| Reference:
|
[5] Serrin J.: On the interior regularity of weak solutions of the Navier-Stokes equations.Arch. Rational Mech. Anal. 9 (1962), 187-195. Zbl 0106.18302, MR 0136885 |
| Reference:
|
[6] Temam R.: Navier-Stokes Equations, Theory and Numerical Analysis.North-Holland Publishing Company, Amsterdam, New York, Oxford, 1979. Zbl 0981.35001, MR 0603444 |
| Reference:
|
[7] Temam R.: Navier-Stokes Equations and Nonlinear Functional Analysis.Society for Industrial and Applied Mathematics, Philadelphia, Pennsylvania, second edition, 1995. Zbl 0833.35110, MR 1318914 |
| . |
