A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

Title:

A geometric improvement of the velocity-pressure local regularity criterion for a suitable weak solution to the Navier-Stokes equations

Creator:

Neustupa, Jiří

Identifier:

https://cdk.lib.cas.cz/client/handle/uuid:a106a96d-a3cf-4bc2-9e82-01982bbe4e2f
uuid:a106a96d-a3cf-4bc2-9e82-01982bbe4e2f
doi:10.21136/MB.2014.144145

Subject:

Navier-Stokes equation, suitable weak solution, and regularity

Type:

model:article and TEXT

Format:

bez média and svazek

Description:

We deal with a suitable weak solution (v, p) to the Navier-Stokes equations in a domain Ω ⊂ R 3 . We refine the criterion for the local regularity of this solution at the point (fx0, t0), which uses the L 3 -norm of v and the L 3/2 -norm of p in a shrinking backward parabolic neighbourhood of (x0, t0). The refinement consists in the fact that only the values of v, respectively p, in the exterior of a space-time paraboloid with vertex at (x0, t0), respectively in a ''small'' subset of this exterior, are considered. The consequence is that a singularity cannot appear at the point (x0, t0) if v and p are “smooth” outside the paraboloid.

Language:

English

Rights:

http://creativecommons.org/publicdomain/mark/1.0/
policy:public

Coverage:

685-698

Source:

Mathematica bohemica | 2014 Volume:139 | Number:4

Harvested from:

CDK

Metadata only:

false