On Local Strong Solutions to the 2D MHD Equations 
with Navier-type Boundary Condition in a Strip

Songshang Yang

doi:https://doi.org/10.14445/22315373/IJMTT-V70I4P103

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 70 | Issue 4 | Year 2024 | Article Id. IJMTT-V70I4P103 | DOI : https://doi.org/10.14445/22315373/IJMTT-V70I4P103

On Local Strong Solutions to the 2D MHD Equations with Navier-type Boundary Condition in a Strip

Songshang Yang

Received	Revised	Accepted	Published
15 Feb 2024	17 Mar 2024	08 Apr 2024	28 Apr 2024

Abstract

This paper presents the local well-posedness of the strong solutions to the 2D incompressible magnetohydrodynamics(MHD) equations without magnetic diffusion in a strip domain. Via a semi-discrete Galerkin scheme, we construct approximate solutions with Navier-type boundary conditions, and can have solutions by passing the limit. Moreover, our results are valid for the Cauchy problem.

Keywords

Magnetohydrodynamics (MHD) equations, A strip domain, Semi-discrete Galerkin scheme, Navier-type boundary condition.

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Citation :

Songshang Yang, "On Local Strong Solutions to the 2D MHD Equations with Navier-type Boundary Condition in a Strip," International Journal of Mathematics Trends and Technology (IJMTT), vol. 70, no. 4, pp. 27-32, 2024. Crossref, https://doi.org/10.14445/22315373/IJMTT-V70I4P103