Stabilization Mechanisms in Magnetohydrodynamics with Partial Dissipation

Speaker：Jiahong Wu (University of Notre Dame)

Time：2026-8-6 15:30

Location：Conference Room C610 at Administration Building at Haiyun Campus

Abstract:

In this talk, we discuss several recent results on global stability and large-time behavior of incompressible and compressible magnetohydrodynamic (MHD) systems. We first consider incompressible MHD equations with partial or anisotropic dissipation, including problems in the whole space and domains with boundaries such as the half-space. We then turn to compressible MHD systems, including non-resistive and partially dissipative models. In these settings, the absence of magnetic diffusion or other dissipative terms creates significant analytical difficulties. By exploiting the coupling among acoustic waves, magnetic fields, and fluid motion, we reveal new mechanisms through which magnetic fields recover missing dissipation and prevent nonlinear instability. The analysis combines spectral methods, anisotropic energy estimates, hidden wave structures, and refined decay techniques.