Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space | Zendy

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Local interior regularity for the 3D MHD equations in nonendpoint borderline Lorentz space

Author(s) -

JaeMyoung Kim

Publication year - 2020

Publication title -

aims mathematics

Language(s) - English

Resource type - Journals

ISSN - 2473-6988

DOI - 10.3934/math.2021148

Subject(s) - lorentz transformation , magnetohydrodynamics , space (punctuation) , lorentz space , closure (psychology) , physics , lorentz force , mathematics , mathematical physics , mathematical analysis , combinatorics , classical mechanics , plasma , magnetic field , quantum mechanics , computer science , law , political science , operating system

We prove local regularity condition for a suitable weak solution to 3D MHD equations. Precisely, if a solution satisfies $u, b \in L^{\infty}(-(\frac{4}{3})^2, 0;L^{3, q}(B_{\frac{3}{4}}))$, $q\in (3, \infty)$ in Lorentz space, then $(u, b)$ is Hölder continuous in the closure of the set $Q_{\frac{1}{2}}$.

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