报告题目：Boundary value problems in plasma dynamics

报 告 人：Diego Alonso-Oran(Ramón y Cajal Researcher @ULL Universidad de La Laguna)

报告时间：2026年6月2日（星期二）13:30 – 15:00；2026年6月3日（星期三）9:00 – 10:30 和 13:30 – 15:00

报告地点：见好就收才是赢太阳9728114（小报告厅）      

校内联系人：廖娴 教授       联系方式：84708351-8510

Abstract: Steady configurations in plasma dynamics are often described by the magneto-hydrostatic equations, which couple the magnetic field, the current density, and the plasma pressure. A classical question is whether such equilibria can be reconstructed from partial boundary data prescribed on suitable inflow and outflow parts of the boundary. This leads to a delicate class of mixed elliptic-transport problems in which the geometry of magnetic field lines plays a central role.

In this mini-course, I will discuss recent analytical progress on this problem, moving from the two-dimensional theory to the genuinely three-dimensional setting. In two dimensions, I will explain how the boundary value problem can be reformulated as a nonlinear fixed-point problem combining transport of the current with a nonlocal reconstruction of the magnetic field. I will then discuss the three-dimensional extension, where the divergence-free character of the current and genuinely three-dimensional transport effects require new tools, including pseudo-differential operators of limited regularity. Time permitting I will also comment on some ongoing work for the  steady MHD equations.