Mathematical Analysis of Free Boundary Problems in EMHD and Related Topics

2016 Fiscal Year Final Research Report

• Project/Area Number: 26400176
• Research Category: Grant-in-Aid for Scientific Research (C)
• Allocation Type: Multi-year Fund
• Section: 一般
• Research Field: Mathematical analysis
• Research Institution: Keio University
• Principal Investigator: Tani Atusi 慶應義塾大学, 理工学部(矢上), 名誉教授 (90118969)
• Co-Investigator(Renkei-kenkyūsha): ITOH Sigeharu 弘前大学, 教育学部, 教授 (40193487) ; TANAKA Naoto 福岡大学, 理学部, 教授 (00247222) ; ITOU Hiromichi 東京理科大学, 理学部第二部, 専任講師 (30400790) ; UMEHARA Morimichi 宮崎大学, 工学部, 准教授 (40532164)
• Project Period (FY): 2014-04-01 – 2017-03-31
• Keywords: free boundary problem / Navier-Stokes equations / Hele-Shaw problem / EMHD / primitive equations / film approximation / drift wave turbulence / gas discharge

Outline of Final Research Achievements

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.

Free Research Field

非線型解析学, 数理物理学