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arXiv · 1501.02085

New look at the Navier-Stokes equation

Tomasz Dlotko
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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.

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Tomasz Dlotko. 2015-01-09. New look at the Navier-Stokes equation. https://arxiv.org/abs/1501.02085

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