2012 Fiscal Year Final Research Report
Bifurcation and structure of solutions for fluid dynamical systems
| Project/Area Number |
22540161
|
|---|
| Research Category |
Grant-in-Aid for Scientific Research (C)
|
| Allocation Type | Single-year Grants |
|---|
| Section | 一般 |
|---|
| Research Field |
General mathematics (including Probability theory/Statistical mathematics)
|
|---|
| Research Institution | Setsunan University |
|---|
Principal Investigator |
|
|---|
| Co-Investigator(Kenkyū-buntansha) |
ITO Keiichi 摂南大学, 理工学部, 教授 (50268489)
SHIMDA Shin-ichi 摂南大学, 理工学部, 准教授 (40196481)
|
|---|
| Co-Investigator(Renkei-kenkyūsha) |
NISHIDA Takaki 京都大学, 情報学研究科, 研究員 (70026110)
|
|---|
| Project Period (FY) |
2010 – 2012
|
| Keywords | ナビエ・ストークス方程式 / ベナール・マランゴニ対流 / 圧縮性熱対流 / 定常・周期解分岐 / 自由表面流 |
|---|
| Research Abstract |
We are concerned mainly with fluid dynamical systems describing motions for compressible heat convection, viscous incompressible flow down an inclined plane or down a vertical plane under the gravity. After constructing resolvent operators and estimating their norms we proved existence of solutions to full nonlinear problems and studied bifurcation structure and stability of solutions. To show existence proof and asymptotic property of bifurcating solutions, it is the key point that those resolvent operator generate an analytic semigroup in a suitable function space. We proved the existence of stationary solution to the compressible heat convection and obtained the bifurcating branch from the heat conducting state.
|
