2014 Fiscal Year Final Research Report
Study on the relation between the mean field of the equilibrium vortices and the vortex system
| Project/Area Number |
22540231
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
Global analysis
|
|---|
| Research Institution | Kanazawa University (2013-2014)
University of Miyazaki (2010-2012) |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
TANAKA Mieko 東京理科大学, 理学部, 助教 (00459728)
TSUJIKAWA Tohru 宮崎大学, 工学部, 教授 (10258288)
YAZAKI Shigetoshi 宮崎大学, 工学部, 准教授 (00323874)
|
|---|
| Research Collaborator |
GLADIALI Francesca
GROSSI Massimo
RICCIARDI Tonia
SUZUKI Takashi
TAKAHASHI Futoshi
YATSUYANAGI Yuichi
|
|---|
| Project Period (FY) |
2010-04-01 – 2015-03-31
|
| Keywords | 関数方程式論 / 変分法 / 点渦 / 渦点 / 平均場 / 数理物理 |
|---|
| Outline of Final Research Achievements |
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.
|
| Free Research Field |
変分問題
|
