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KAKEN_23654055seika.pdf
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Title |
Title |
非ニュートン流体の運動の数学解析
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Kana |
ヒニュートン リュウタイ ノ ウンドウ ノ スウガク カイセキ
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Romanization |
Hinyuton ryutai no undo no sugaku kaiseki
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Mathematical analysis of the non-Newtonian fluids flow
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谷, 温之
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Kana |
タニ, アツシ
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Romanization |
Tani, Atusi
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Affiliation |
慶應義塾大学・理工学部・名誉教授
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Research team head
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科研費研究者番号 : 90118969
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Name |
井口, 達雄
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Kana |
イグチ, タツオ
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Romanization |
Iguchi, Tatsuo
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Affiliation |
慶應義塾大学・理工学部・教授
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Research team member
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科研費研究者番号 : 20294879
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Name |
高山, 正宏
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Kana |
タカヤマ, マサヒロ
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Romanization |
Takayama, Masahiro
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Affiliation |
慶應義塾大学・理工学部・助教
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Research team member
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科研費研究者番号 : 90338252
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Name |
野寺, 隆
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Kana |
ノデラ, タカシ
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Romanization |
Nodera, Takashi
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Affiliation |
慶應義塾大学・理工学部・教授
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Affiliation (Translated) |
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Research team member
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Link |
科研費研究者番号 : 50156212
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Name |
伊藤, 茂治
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Kana |
イトウ, シゲハル
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Romanization |
Ito, Shigeharu
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Affiliation |
弘前大学・教育学部・教授
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Research team member
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科研費研究者番号 : 40193487
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田中, 尚人
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Kana |
タナカ, ナオト
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Romanization |
Tanaka, Naoto
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Affiliation |
福岡大学・理学部・教授
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Research team member
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科研費研究者番号 : 00247222
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伊藤, 弘道
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Kana |
イトウ, ヒロミチ
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Romanization |
Ito, Hiromichi
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Affiliation |
東京理科大学・理学部第二部・専任講師
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Research team member
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科研費研究者番号 : 30400790
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梅原, 守道
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Kana |
ウメハラ, モリミチ
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Romanization |
Umehara, Morimichi
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Affiliation |
宮崎大学・工学部・准教授
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Research team member
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科研費研究者番号 : 40532164
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Issued (from:yyyy) |
2015
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科学研究費補助金研究成果報告書
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2014
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Abstract |
非ニュートン流体運動として記述される自然諸現象のモデル方程式に対する非線形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) 非ニュートン流体, 特に流れ学的構成則がジャヌマン共回転微分を持つ非圧縮粘弾性マックスウエル媒質中の2次元流が, 滑らかな初期値に対しても, 不連続性が生じ得ることを示し, その衝撃波の安定性について考察した。(2) 2次元斉次等方的弾性体内部に剛体線状亀裂があるとき, 層間剥離の生起, 不生起両場合に対し, その先端部分での漸近挙動を調べた。(3) 境界濡れ効果下でのヘレ-ショウセル中のフィンガリング現象に対して弱非線形解析を行った。
Well-posedness of nonlinear problems for various natural phenomena, especially of those described as non-Newtonian fluids flow was established mathematically. Some of research results are as follows.
(1) For a non-Newtonian fluid flow, especially for the 2-dimensional flow of incompressible viscoelastic Maxwell media with a Jaumann corotational derivative in the rheological constitutive law we proved that the discontinuity can develop even from smooth initial data, and the stability of shocks in it without retardation. (2) An equilibrium problem for 2-dimensional homogeneous isotropic linearized elasticity with a rigid line inclusion was studied in both not delaminated and laminated cases, and investigated an asymptotic behavior of a solution near a tip of a rigid line inclusion. (3) The fingering pattern of radially growing interface in a Hele-Shaw cell was shown in the framework of weakly nonlinear analysis under the wetting layer effect of the displacing fluid taken into account.
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研究種目 : 挑戦的萌芽研究
研究期間 : 2011~2014
課題番号 : 23654055
研究分野 : 非線形解析, 数理物理
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