Research projects

Well-posedness of various nonlinear and free boundary problems in EMHD and its related fields was established mathematically. Some of the research results are as follows. (1) Free boundary problem for two-phase classical MHD for viscous and compressible fluids has been studied and proved to admit a unique local-in-time classical solution. (2) In the phenomenon of gas discharge the model system of PDEs due to Degon, Lucquin, Desreux and Morrow are investigated mathematically and established its unique solvability locally in time. (3) The fingering pattern of radially growing interface in a Hele-Shaw cell was shown in the framework of Hoelder spaces under surface tension effect on the interface between the displacing and displaced fluids taken into account through the parabolic regularization method. (4) Free boundary problem for two-phase, atmosphere and ocean, primitive equations has discussed and shown the existence of a unique strong solution locally in time.