On 3D generalized MHD equations with different dissipation exponents

We study the 3D generalized magnetohydrodynamics (gMHD) equations with dissipation terms -(- increment )& alpha;u and -(- increment )& beta;b. It is proved that a weak solution (u, b) to gMHD equations is smooth on 1[83 x (0, T] if u, Vu or (- increment )m/2u belongs to Lq(0,T; Lp(1[83)) with p, q and m = min{& alpha;, & beta;} satisfying the generalized Ladyzhenskaya-Prodi-Serrin type conditions. & COPY; 2023 Elsevier Ltd. All rights reserved.

Automated summary

This paper studies the 3D generalized magnetohydrodynamics (gMHD) equations with dissipation terms. It is proved that a weak solution (u, b) to gMHD equations is smooth on 1[83 x (0, T] if u, Vu or (- increment )m/2u belongs to Lq(0,T; Lp(1[83)) with p, q and m = min{& alpha;, & beta;} satisfying the generalized Ladyzhenskaya-Prodi-Serrin type conditions.