Several almost critical regularity conditions based on one component of the solutions for 3D N-S Equations

preprint2013arXivOpen access

Abstract

In this article, we establish several almost critical regularity conditions such that the weak solutions of the 3D Navier-Stokes equations become regular, based on one component of the solutions, say u3u_3 and ∂3u3\partial_3u_3.

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