The magnetohydrodynamical system in bounded non smooth domains of dimension n≥3

2025/07/24 by Sylvie Monniaux, Monniaux, Sylvie
Mathematics · #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Geometric Analysis and Curvature Flows #Navier-Stokes equation solutions

paper · pdf · doi:10.48550/arxiv.2507.18195

openalex publication_date 2025/07/24 · openalex created_date 2025/10/16 · openalex updated_date 2026/08/02

Abstract

Existence of mild solutions for the magnetohydrodynamical system in C 1 domains is established in critical spaces in dimension n ≥3. The proof relies on recent regularity results on the Stokes operator in C 1 domains and a Leibniz-like formula for differential forms proved here in Section 2.

Citations

• Existence in critical spaces for the magnetohydrodynamical system in 3D bounded Lipschitz domains
• Solutions of Navier--Stokes--Maxwell systems in large energy spaces
• On the L^p-theory of the Navier--Stokes equations on three-dimensional bounded Lipschitz domains
• Hodge-Dirac, Hodge-Laplacian and Hodge-Stokes operators in L^p spaces on Lipschitz domains
• Global Well-posedness of the Incompressible Magnetohydrodynamics
• Global Well-Posedness of the Incompressible Magnetohydrodynamics
• Local existence for the non-resistive MHD equations in Besov spaces
• Higher order commutator estimates and local existence for the non-resistive MHD equations and related models

Related

• Existence in critical spaces for the magnetohydrodynamical system in 3D bounded Lipschitz domains
• Existence and uniqueness in critical spaces for the magnetohydrodynamical system in ℝⁿ
• Global mild solutions to three-dimensional magnetohydrodynamic system in\n Morrey spaces
• Global existence for the MHD system in critical spaces
• A geometric measure-type regularity criterion for solutions to the magnetohydrodynamical system