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KAKEN_26400176seika  
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Title
Title EMHDとそれに関連する自由境界問題の数学解析  
Kana EMHD ト ソレニ カンレンスル ジユウ キョウカイ モンダイ ノ スウガク カイセキ  
Romanization EMHD to soreni kanrensuru jiyu kyokai mondai no sugaku kaiseki  
Other Title
Title Mathematical analysis of free boundary problems in EMHD and related topics  
Kana  
Romanization  
Creator
Name 谷, 温之  
Kana タニ, アツシ  
Romanization Tani, Atsushi  
Affiliation 慶應義塾大学・理工学部・名誉教授  
Affiliation (Translated)  
Role Research team head  
Link 科研費研究者番号 : 90118969

Name 井口, 達雄  
Kana イグチ, タツオ  
Romanization Iguchi, Tatsuo  
Affiliation 慶應義塾大学・理工学部・教授  
Affiliation (Translated)  
Role Research team member  
Link 科研費研究者番号 : 20294879

Name 野寺, 隆  
Kana ノデラ, タカシ  
Romanization Nodera, Takashi  
Affiliation 慶應義塾大学・理工学部・教授  
Affiliation (Translated)  
Role Research team member  
Link 科研費研究者番号 : 50156212

Name 伊藤, 茂治  
Kana イトウ, シゲハル  
Romanization Ito, Shigeharu  
Affiliation 弘前大学・教育学部・教授  
Affiliation (Translated)  
Role Research team member  
Link 科研費研究者番号 : 40193487

Name 田中, 尚人  
Kana タナカ, ナオト  
Romanization Tanaka, Naoto  
Affiliation 福岡大学・理学部・教授  
Affiliation (Translated)  
Role Research team member  
Link 科研費研究者番号 : 00247222

Name 伊藤, 弘道  
Kana イトウ, ヒロミチ  
Romanization Ito, Hiromichi  
Affiliation 東京理科大学・理学部第二部・専任講師  
Affiliation (Translated)  
Role Research team member  
Link 科研費研究者番号 : 30400790

Name 梅原, 守道  
Kana ウメハラ, モリミチ  
Romanization Umehara, Morimichi  
Affiliation 宮崎大学・工学部・准教授  
Affiliation (Translated)  
Role Research team member  
Link 科研費研究者番号 : 40532164
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Date
Issued (from:yyyy) 2017  
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Physical description
1 pdf  
Source Title
Name 科学研究費補助金研究成果報告書  
Name (Translated)  
Volume  
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Year 2016  
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Doctoral dissertation
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Abstract
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.
 
Table of contents

 
Keyword
free boundary problem  

Navier-Stokes equations  

Hele-Shaw problem  

EMHD  

primitive equations  

film approximation  

drift wave turbulence  

gas discharge  
NDC
 
Note
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
 
Language
日本語  

英語  
Type of resource
text  
Genre
Research Paper  
Text version
publisher  
131.113.194.249
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Last modified date
Sep 21, 2017 15:41:02  
Creation date
Sep 21, 2017 15:41:02  
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History
 
Index
/ Public / Grants-in-Aid for Scientific Research / Fiscal year 2016 / Japan Society for the Promotion of Science
 
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