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

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 $\int |\nabla v{|}^{2}dx$.

arXiv commentThis paper has been withdrawn by the author due to a crucial sign error in equation 1