We had intensive lectures (90min × 6) by Professor Elena Frolova (St. Petersburg State University and St. Petersburg Electrotechnical University) from January 23 to February 08. In the lecture, she explained the proof of the local/global unique solvability of the free boundary problem of the two-phase Magneto Hydro Dynamics (MHD) equation. This equation describes the motion of fluid metal (eg. mercury) and plasma, which considers the interaction between fluid flow and electromagnetic field.
As for the results of the two-phase MHD equation, there is a lot of results mainly due to the Russian school including Professor Elena Frolova. We know that the free boundary problem is difficult because we have to find not only the unknown velocity but also unknown boundary. Although the free boundary problem is difficult, this model is closer to the actual physical model than the usual “fixed” boundary problem, so that, recently, the free boundary problem is one of the hot research topics.
Professor Elena Frolova is one of the great mathematicians who leads the free boundary problem of two-phase MHD and has presented a lot of results. There were some students who did not major in mathematics, but thankfully for her kindness, she gave us a very plain lecture that everyone could understand. The lectures were very interesting and educational and good opportunity to learn the most-advanced mathematical techniques.