Geodesic
On the local regularity theory for the magnetohydrodynamic equations
Documenta mathematica, Tome 26 (2021), pp. 125-148.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Local regularity results are obtained for the MHD equations using as global framework the setting of parabolic Morrey spaces. Indeed, by assuming some local boundedness assumptions (in the sense of parabolic Morrey spaces) for weak solutions of the MHD equations it is possible to obtain a gain of regularity for such solutions in the general setting of the Serrin regularity theory. This is the first step of a wider program that aims to study both local and partial regularity theories for the MHD equations.
Classification : 35Q35, 42B37, 35B65, 35D30, 76W05
Keywords: MHD equations, parabolic Morrey spaces, local regularity theory 
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     author = {Chamorro, Diego and Cortez, Fernando and He, Jiao and Jarr{\'\i}n, Oscar},
     title = {On the local regularity theory for the magnetohydrodynamic equations},
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Chamorro, Diego; Cortez, Fernando; He, Jiao; Jarrín, Oscar. On the local regularity theory for the magnetohydrodynamic equations. Documenta mathematica, Tome 26 (2021), pp. 125-148. http://geodesic.mathdoc.fr/item/DOCMA_2021__26__a53/