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Stability and long-time behavior for the 2D anisotropic MHD equations with partial magnetic damping

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  • Xu, Bo
  • Wu, Fan
  • Zhou, Jiang

Abstract

This paper investigates the stability and long-time behavior to the 2D magnetohydrodynamics (MHD) equations with partial dissipation and damping. In this setting, the velocity field is subject to anisotropic dissipation, while magnetic damping acts only on the vertical component. The absence of full dissipation and damping poses substantial challenges for establishing global well-posedness. Exploiting the stabilizing mechanism induced by the background magnetic field, we construct a new energy functional and employ wave-type estimates to prove the global stability of any perturbation near the background magnetic field (0,1) in the Sobolev space H2(R2). Furthermore, the long-time behavior of these solutions is rigorously derived.

Suggested Citation

  • Xu, Bo & Wu, Fan & Zhou, Jiang, 2026. "Stability and long-time behavior for the 2D anisotropic MHD equations with partial magnetic damping," Chaos, Solitons & Fractals, Elsevier, vol. 202(P2).
    • Handle: RePEc:eee:chsofr:v:202:y:2026:i:p2:s0960077925015887
    DOI: 10.1016/j.chaos.2025.117575
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