Existence of infinite-energy and discretely self-similar global weak solutions for 3D MHD equations

Pedro Gabriel Fernández-Dalgo (1) , Oscar Jarrin (2)

1 LaMME - Laboratoire de Mathématiques et Modélisation d'Evry
2 Universidad Técnica de Ambato

This paper deals with the existence of global weak solutions for 3D MHD equations when the initial data belong to the weighted spaces $L^2_{w_\gamma}$, with $w_\gamma(x)=(1+\vert x\vert)^{-\gamma}$ and $0 \leq \gamma \leq 2$. Moreover, we prove the existence of discretely self-similar solutions for 3D MHD equations for discretely self-similar initial data which are locally square integrable. Our methods are inspired of a recent work of P. Fern\'aidez-Dalgo and P.G. Lemarié-Rieusset for the 3D Navier-Stokes equations.

Mots clés: MHD equations; weighted L 2 spaces; energy controls; discretely self-similar solutions

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]

Pedro Gabriel Fernández-Dalgo, Oscar Jarrin. Existence of infinite-energy and discretely self-similar global weak solutions for 3D MHD equations. 2019. ⟨hal-02332520⟩