Journal
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK
Volume 72, Issue 1, Pages -Publisher
SPRINGER INTERNATIONAL PUBLISHING AG
DOI: 10.1007/s00033-020-01442-1
Keywords
Regularity criteria; Navier-Stokes equations; Regularity of solutions
Categories
Funding
- National Natural Science Foundation of China [11761009]
- Natural Science Foundation of Jiangxi Province [20202BABL201008]
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It is proven that the solution to the Navier-Stokes system is smooth under specific conditions regarding the Sobolev spaces L-p and L-q, which improves upon previous research findings.
It is proved that if the solution of the Navier-Stokes system satisfies partial derivative(3)u is an element of L-p(0, T; L-q(R-3)), 2/p + 3/q = 22/13 + 3/13q, 3 < q < 4, or partial derivative(3)u(3) is an element of L-beta(0, T; L-alpha(R-3)), 2/beta + 3/alpha = 3(root 65 alpha(2) - 78 alpha + 49 + 7 - alpha)/16 alpha, 3+root 17/4 <= alpha <= infinity, then the solution is smooth on (0, T]. These two improve many previous results.
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