Periodic solutions of the 3D MHD equations in bounded domains with arbitrary geometry
Abstract
We show existence and uniqueness of strong periodic solutions to the magnetohydrodynamic (MHD) equations in an arbitrary 3D bounded domain Ω with smooth boundary ∂Ω. It should be emphasized that we do not need to impose any geometric condition on Ω. Based on the L r -theorem of the magnetic Laplace operator by [14] , we develop the method of [11] for construction of global mild solutions with small periodic external forces. We also prove that our solution becomes necessarily regular provided the given data are certainly smooth.
Fields of Study & Subjects
Navier-Stokes equation solutions
Nonlinear Partial Differential Equations
Advanced Mathematical Modeling in Engineering
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Publisher
- Elsevier BV
- Volume
- 564
- Issue
- 1
- Pages
- 130830–130830
- Publication date
- 29 May 2026
- Language
- EN