EMHDとその関連分野における非線形問題, 自由境界問題の適切性を数学解析面から研究した。具体的研究成果の一部を記す。(1) 圧縮性Navier-Stokes方程式に対する古典的MHD2相自由境界問題の時間局所古典解の一意存在を考察した。(2) ガス放電現象に対するDegon-Lucquin-Desreux-Morrowモデル方程式の時間局所一意強可解性を証明した。(3) Hele-Shaw問題に関して, 表面張力効果なし2相問題の時間局所古典解存在を放物型正則化問題経由で証明した。(4)大気/海洋2相primitive方程式系の自由境界問題に対する時間局所一意強可解性を証明した。
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.

研究種目 : 基盤研究(C)(一般)
研究期間 : 2014～2016
課題番号 : 26400176
研究分野 : 非線型解析学, 数理物理学