Stability and Long-Time Dynamics of Anisotropic 3D MHD Near a Background Magnetic Field
报告人：吴家宏 ( University of Notre Dame)
时间：2026-01-04 14:30-15:30
地点：智华楼王选报告厅
Abstract: The 3D incompressible Navier-Stokes with dissipation in a single direction in R^3 is not well-understood, and the small data global well-posedness problem remains open. However, when this Navier-Stokes is coupled with the equation of the magnetic field, the resulting MHD system has been shown to be globally well-posed near a background magnetic field. In addition, the perturbation decays with 2D heat-like behaviors. This reveals the stabilizing and damping effect of the magnetic field. Even in domains with simple boundary such as the half space, these mechanisms persist and allow global-in-time uniform bounds, well-posedness and decay near a background magnetic field.
