Stability of Two-Dimensional Incompressible MHD 
Equations with Mixed Partial Dissipation

Gaofeng Wu

doi:https://doi.org/10.14445/22315373/IJMTT-V71I7P108

International Journal of Mathematics Trends and Technology

Research Article | Open Access | Download PDF

Volume 71 | Issue 7 | Year 2025 | Article Id. IJMTT-V71I7P108 | DOI : https://doi.org/10.14445/22315373/IJMTT-V71I7P108

Stability of Two-Dimensional Incompressible MHD Equations with Mixed Partial Dissipation

Gaofeng Wu

Received	Revised	Accepted	Published
25 May 2025	30 Jun 2025	17 Jul 2025	28 Jul 2025

Citation :

Gaofeng Wu, "Stability of Two-Dimensional Incompressible MHD Equations with Mixed Partial Dissipation," International Journal of Mathematics Trends and Technology (IJMTT), vol. 71, no. 7, pp. 79-97, 2025. Crossref, https://doi.org/10.14445/22315373/IJMTT-V71I7P108

Abstract

This paper investigates the stabilization effect of the two-dimensional incompressible MHD system with partial dissipation near a background magnetic field. Employing time-global uniform a priori estimates, we establish the global well-posedness of the nonlinear MHD equations in𝐻3(ℝ2). Building upon this fundamental result, we derive the large-time asymptotic behavior of the solutions.

Keywords

MHD equations; stability; large-time behavior.

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