A remark on the partial regularity of a suitable weak solution to the Navier-Stokes Cauchy problem

2015/07/23 by Crispo, Francesca, Maremonti, Paolo · 1 citation
#FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1507.06436

Abstract

Starting from the partial regularity results for suitable weak solutions to the Navier-Stokes Cauchy problem by Caffarelli, Kohn and Nirenberg, as a corollary, under suitable assumptions of local character on the initial data, we prove a behavior in time of the L^∞_loc-norm of the solution in a neighborhood of t=0. The behavior is the same as for the resolvent operator associated to the Stokes operator. Besides its own interest, the result is a main tool to study the spatial decay estimates of a suitable weak solution, performed in paper F. Crispo and P. Maremonti, On the spatial asymptotic decay of a suitable weak solution to the Navier-Stokes Cauchy problem (submitted).

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