New look at the Navier-Stokes equation
Abstract
We propose a new way of looking at the Navier-Stokes equation (N-S) in dimensions two and three. We consider its regular approximations in which the -P Delta operator is replaced with the fractional power. The 3-D N-S equation is super-critical with respect to the standard L2 a priori estimates; the regular approximating problem in 3-D should contain fractional power with s > 5/4. Using Dan Henry's semigroup approach we construct regular solutions to such approximations. The solutions are unique, smooth and regularized through the equation in time. Solution to 2-D and 3-D N-S equations are obtained next as a limit of the regular solutions of the above approximations.
Cite
@article{arxiv.1501.02085,
title = {New look at the Navier-Stokes equation},
author = {Tomasz Dlotko},
journal= {arXiv preprint arXiv:1501.02085},
year = {2015}
}
Comments
I am sending the final, completed version of the manuscript; New look at the Navier-Stokes equation that is carefully checked and extended with few remarks presented in the final part. I also hope that the manuscript will be soon accepted for publication in the Journal it was submitted early this year. Tomasz Dlotko