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Keywords:
Navier-Stokes equations; suitable weak solutions; local regularity
Navier-Stokes equations; suitable weak solutions; local regularity
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.
References:
[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. MR 0673830 | Zbl 0509.35067
[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.
[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. MR 1738171 | Zbl 0954.35129
[4] Lin F.: A new proof of the Caffarelli-Kohn-Nirenberg Theorem. Comm. Pure Appl. Math. 51 (1998), 241-257. MR 1488514 | Zbl 0958.35102
[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
[6] Neustupa J.: A removable singularity of a suitable weak solution to the Navier-Stokes equations. preprint.
[7] Nečas J., Neustupa J.: New conditions for local regularity of a suitable weak solution to the Navier-Stokes equations. preprint.
[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.
[9] Temam R.: Navier-Stokes Equations, Theory and Numerical Analysis. North-Holland Publishing Company, Amsterdam, New York, Oxford, revised edition, 1979. MR 0603444 | Zbl 0981.35001
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