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

2019/10/24 by Pedro Gabriel Fernández-Dalgo, Fernández-Dalgo, Pedro Gabriel, Oscar Jarrín +1
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.1910.11267

openalex publication_date 2019/10/24 · openalex created_date 2019/11/01 · openalex updated_date 2026/07/28

Abstract

This paper deals with the existence of global weak solutions for 3D MHD equations when the initial data belong to the weighted spaces L²_wγ, with w_γ(x)=(1+| x|)^-γ and 0 ≤ γ≤ 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. Fernández-Dalgo and P.G. Lemarié-Riseusset for the 3D Navier-Stokes equations.

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