Global existence and uniqueness of weak solutions of a Stokes-Magneto system with fractional diffusions

초록

We consider a Stokes-Magneto system in R-d (d > 2) with fractional diffusions A(2 alpha)u and A(2 beta)b for the velocity u and the magnetic field b, respectively. Here alpha, beta are positive constants and A(s) = (-A)(s/2) is the fractional Laplacian of order s. We establish global existence of weak solutions of the Stokes-Magneto system for any initial data in L-2 when alpha, beta satisfy 1/2 < alpha < (d + 1)/2, beta> 0, and min{alpha + beta, 2 alpha + beta - 11 > d/2. It is also shown that weak solutions are unique if beta >= 1 and min{alpha + beta, 2 alpha + beta - 11 >= d/2 + 1, in addition. (c) 2023 Elsevier Inc. All rights reserved.

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