Discretely Self-Similar Solutions for 3D MHD Equations and Global Weak Solutions in Weighted L² Spaces

Abstract:

This paper deals with the existence of global weak solutions for 3D MHD equations when the initial data belong to the weighted spaces Lwγ2, with wγ(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 (Fernández-Dalgo et al. in Arch Rational Mech Anal 237:347–382, 2020) for the Navier–Stokes equations.

Año de publicación:

2021

Keywords:

• Discretely self-similar solutions
• Weighted L spaces 2
• MHD equations
• Energy controls

Fuente:

scopus