平衡点渦系の平均場と点渦系の関連の探求

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Author: 大塚, 浩史ほか

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Publication date: 2015-06-10

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Note (General)：: 金沢大学理工研究域数物科学系点渦系の平衡平均場を与える汎関数のグラフの構造を、点渦系のハミルトニアンと関連づけて考察した。主たる成果は、平均場の爆発列と爆発極限に現れる定常点渦系（ハミルトニアンの臨界点）が与えられたとき、その定常点渦系のモース指数を用いて、爆発に十分近づいた平均場（汎関数の臨界点）...

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https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540231/

https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-22540231/22540231seika/

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Material Type: 文書・図像類
Title: 平衡点渦系の平均場と点渦系の関連の探求
Author/Editor: 大塚, 浩史
Ohtsuka, Hiroshi
Author Heading: 大塚, 浩史
Ohtsuka, Hiroshi
Publication Date: 2015-06-10
Publication Date (W3CDTF): 2015-06-10
Alternative Title: Study on the relation between the mean field of the equilibrium vortices and the vortex system
Periodical title: 平成26(2014)年度科学研究費補助金基盤研究(C) 研究成果報告書 = 2014 Fiscal Year Final Research Report
No. or year of volume/issue: 2010-04-01 - 2015-03-31
Volume: 2010-04-01 - 2015-03-31
Pages: 4p.-
Text Language Code: jpn
Subject Heading: 関数方程式論
変分法
点渦
渦点
平均場
数理物理
Target Audience: 一般
Note (General): 金沢大学理工研究域数物科学系
点渦系の平衡平均場を与える汎関数のグラフの構造を、点渦系のハミルトニアンと関連づけて考察した。主たる成果は、平均場の爆発列と爆発極限に現れる定常点渦系（ハミルトニアンの臨界点）が与えられたとき、その定常点渦系のモース指数を用いて、爆発に十分近づいた平均場（汎関数の臨界点）のモース指数を評価する不等式を与えたことである。考察した平均場は、通常の自由エネルギー汎関数を簡略化した汎関数から得られるもの（ゲルファント問題の解）だが、平均場が１点爆発する場合を示した既知の結果を拡張し、多点爆発する一般の場合について結論を得た。関連して、ゲルファント問題の線形化固有値の一部について、精密な挙動を与えた。
I studied the structure of the graph of the functional for mean fields of equilibrium vortices in terms of the Hamiltonian of vortices. A mean field is a critical point of a functional and steady vortices form a critical point of a function (Hamiltonian). The main result is to determine the inequalities that estimate the Morse index of the mean field, which is sufficiently close to blow-up, in terms of the Morse index of the steady vortices, when a blow-up sequence of mean fields and the steady vortices in its blow-up limit are given. The mean fields that I consider are solutions of the Gel’fand problem, which comes from the functional that is rather simplified one from the usual free energy functional for mean fields. Our conclusion, however, generalize the known result that treats one point blow-up cases only to general many points blow-up cases. I also give some fine behaviors of linearized eigenvalues of Gel’fand problem.
研究課題/領域番号:22540231, 研究期間(年度):2010-04-01 - 2015-03-31
DOI: 10.24517/00052465
Access Restrictions: 限定公開
Related Material: https://kaken.nii.ac.jp/search/?qm=20342470
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-22540231/
https://kaken.nii.ac.jp/report/KAKENHI-PROJECT-22540231/22540231seika/
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 金沢大学 : 金沢大学学術情報リポジトリKURA