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A regularity criterion for positive part of radial component in the case of axially symmetric Navier-Stokes equations

Kubica A.

Demonstratio Mathematica

2015

Vol. 48, nr 1

62--72

We examine the conditional regularity of the solutions of Navier–Stokes equations in the entire three-dimensional space under the assumption that the data are axially symmetric. We show that if positive part of the radial component of velocity satisfies a weighted Serrin type condition and in addition angular component satisfies some condition, then the solution is regular.