Existence and uniqueness in critical spaces for the magnetohydrodynamical system in R n

Clément Denis (1, 2, 3)

1 I2M - Institut de Mathématiques de Marseille
2 AMU - Aix Marseille Université
3 CNRS - Centre National de la Recherche Scientifique

We give a description of a magnetohydrodynamical system in n dimension using the exterior derivative. We then prove existence of global solutions for small initial data and local existence for arbitrary large data in two classes of critical spaces-L q t L p x and C t L p x , as well as uniqueness for solutions in C t L p x .

Domaines: Equations aux dérivées partielles [math.AP]

Clément Denis. Existence and uniqueness in critical spaces for the magnetohydrodynamical system in R n. 2022. ⟨hal-03660738v1⟩