2015/01/09 by Dlotko, Tomasz
#35A25 #35Q30 #35S15 #76D05 #FOS: Physical sciences #Mathematical Physics (math-ph)
paper · doi:10.48550/arxiv.1501.02085
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.