The Navier-Stokes equations. Regularity of fast flows and Sobolev imbedding

2014/09/26 by Piotr B. Mucha, Mucha, Piotr B.
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP

paper · pdf · doi:10.48550/arxiv.1409.7536

This paper has been withdrawn by the author due to a crucial sign error in equation 1

arxiv created 2014/10/30 · arxiv updated 2014/10/31

Abstract

The paper proves existence of a large class of smooth solutions to the incompressible Navier-Stokes equations in the three dimensional space. The viscosity coefficient is put to be 1. Our result points a new class of regular solutions with arbitrary large Cauchy integral ∫ |∇ v|² dx.

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