| Title:
|
Conditions of Prodi-Serrin's type for local regularity of suitable weak solutions to the Navier-Stokes equations (English) |
| Author:
|
Skalák, Zdeněk |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
43 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
619-639 |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the context of suitable weak solutions to the Navier-Stokes equations we present local conditions of Prodi-Serrin's type on velocity ${\bold v}$ and pressure $p$ under which $({\bold x}_0,t_0)\in \Omega \times (0,T)$ is a regular point of ${\bold v}$. The conditions are imposed exclusively on the outside of a sufficiently narrow space-time paraboloid with the vertex $({\bold x}_0,t_0)$ and the axis parallel with the $t$-axis. (English) |
| Keyword:
|
Navier-Stokes equations |
| Keyword:
|
suitable weak solutions |
| Keyword:
|
local regularity |
| MSC:
|
35B65 |
| MSC:
|
35Q10 |
| MSC:
|
35Q30 |
| MSC:
|
76D05 |
| idZBL:
|
Zbl 1090.35148 |
| idMR:
|
MR2045785 |
| . |
| Date available:
|
2009-01-08T19:25:44Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119352 |
| . |
| Reference:
|
[1] Caffarelli L., Kohn R., Nirenberg L.: Partial regularity of suitable weak solutions of the Navier-Stokes equations.Comm. Pure Apl. Math. 35 (1982), 771-831. Zbl 0509.35067, MR 0673830 |
| Reference:
|
[2] Kučera P., Skalák Z.: Smoothness of the velocity time derivative in the vicinity of regular points of the Navier-Stokes equations.Proceedings of the $4^{th}$ Seminar ``Euler and Navier-Stokes Equations (Theory, Numerical Solution, Applications)'', Institute of Thermomechanics AS CR, Editors: K. Kozel, J. Příhoda, M. Feistauer, Prague, 2001, pp.83-86. |
| Reference:
|
[3] Ladyzhenskaya O.A., Seregin G.A.: On partial regularity of suitable weak solutions to the three-dimensional Navier-Stokes equations.J. Math. Fluid Mech. 1 (1999), 356-387. Zbl 0954.35129, MR 1738171 |
| Reference:
|
[4] Lin F.: A new proof of the Caffarelli-Kohn-Nirenberg Theorem.Comm. Pure Appl. Math. 51 (1998), 241-257. Zbl 0958.35102, MR 1488514 |
| Reference:
|
[5] Neustupa J.: Partial regularity of weak solutions to the Navier-Stokes equations in the class $L^\infty(0,T,L^3(Ømega)^3)$.J. Math. Fluid Mech. 1 (1999), 309-325. MR 1738173 |
| Reference:
|
[6] Neustupa J.: A removable singularity of a suitable weak solution to the Navier-Stokes equations.preprint. |
| Reference:
|
[7] Nečas J., Neustupa J.: New conditions for local regularity of a suitable weak solution to the Navier-Stokes equations.preprint. |
| Reference:
|
[8] Skalák Z.: Removable Singularities of Weak Solutions of the Navier-Stokes Equations.Proceedings of the $4^{th}$ Seminar ``Euler and Navier-Stokes Equations (Theory, Numerical Solution, Applications)'', Institute of Thermomechanics AS CR, Editors: K. Kozel, J. Příhoda, M. Feistauer, Prague, 2001, pp.121-124. |
| Reference:
|
[9] Temam R.: Navier-Stokes Equations, Theory and Numerical Analysis.North-Holland Publishing Company, Amsterdam, New York, Oxford, revised edition, 1979. Zbl 0981.35001, MR 0603444 |
| . |
