We assume that Ω is either the whole space R3 or a half-space or a smooth bounded or exterior domain in R3, T>0 and (u,b,p) is a suitable weak solution of the MHD equations in Ω×(0,T). We show that (x0,t0)∈Ω×(0,T) is a regular point of the solution (u,b,p) if the limit inferior (for t→t0−) of the sum of the L3–norms of u and b over an arbitrarily small ball Bρ(x0) is less than infinity.
|Journal||Journal of Mathematical Analysis and Applications|
|Publication status||Published - 2021 Oct 15|
Bibliographical noteFunding Information:
The first author has been supported by the Academy of Sciences of the Czech Republic ( RVO 67985840 ) and by the Grant Agency of the Czech Republic , grant No. GA19-04243S . The second author acknowledges the support of the National Research Foundation of Korea No. 2016R1C1B2015731 , No. 2015R1A5A1009350 , and the support of the Yonsei University No. 2019-22-0034 .
© 2021 Elsevier Inc.
All Science Journal Classification (ASJC) codes
- Applied Mathematics