A global existence result for the anisotropic magnetohydrodynamical systems

Van-Sang Ngo (1)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem

We study an anisotropic system arising in magnetohydrodynamics (MHD) in the whole space R^3 , in the case where there are no diffusivity in the vertical direction and only a small diffusivity in the horizontal direction (of size εα with 0 < α ≤ α0, for some α0 > 0). We prove the local existence and uniqueness of a strong solution and then, using Strichartz-type estimates, we prove that this solution globally exists in time for large initial data, when the rotation is fast enough.

Domaines: Equations aux dérivées partielles [math.AP]

Van-Sang Ngo. A global existence result for the anisotropic magnetohydrodynamical systems. 2011. ⟨hal-00599675v1⟩