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

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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.
DOI : 10.4171/dm/811
Classification : 35B65, 35D30, 35Q35, 42B37, 76W05
Mots-clés : MHD equations, parabolic Morrey spaces, local regularity theory 
Fernando Cortez; Jiao He; Diego Chamorro; Oscar Jarrín. On the local regularity theory for the magnetohydrodynamic equations. Documenta mathematica, Tome 26 (2021), pp. 125-148. doi: 10.4171/dm/811
@article{10_4171_dm_811,
     author = {Fernando Cortez and Jiao He and Diego Chamorro and Oscar Jarr{\'\i}n},
     title = {On the local regularity theory for the magnetohydrodynamic equations},
     journal = {Documenta mathematica},
     pages = {125--148},
     year = {2021},
     volume = {26},
     doi = {10.4171/dm/811},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/811/}
}
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