Studies on mathematical structure of boundary value problems appearing in hydrodynamics and magnetohydrodynamics
Project/Area Number |
15K04957
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Research Category |
Grant-in-Aid for Scientific Research (C)
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Allocation Type | Multi-year Fund |
Section | 一般 |
Research Field |
Mathematical analysis
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Research Institution | Nara Women's University |
Principal Investigator |
|
Project Period (FY) |
2015-04-01 – 2018-03-31
|
Project Status |
Completed (Fiscal Year 2017)
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Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2017: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2016: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2015: ¥2,210,000 (Direct Cost: ¥1,700,000、Indirect Cost: ¥510,000)
|
Keywords | 境界値問題 / MHD方程式 / 安定性 / Hodge分解 / 調和ベクトル場 / Navier-Stokes方程式 / MHD / 自由境界 / Nash-Moser型陰関数定理 / 定常解 / 自由境界問題 |
Outline of Final Research Achievements |
This research was intended as an attempt to study the relations, from a mathematical standpoint, between the following three issues on the boundary value problems appearing in the hydrodynamics and magnetohydrodynamics (MHD) : (i) the nonlinear structure of equations, (ii) the setting of boundary conditions, (iii) the geometrical structure of domains. Our results obtained in this reserach can be listed below. (1) We proved the existence and the stability of weak solutions of stationary MHD equations under inhomogeneous boundary conditions.(2) We gave a characterization of harmonic vector fields in three dimensional exterior domain by topological invariants of exterior domains. This result shall be a base for establishing Hodge decomposition theorem for exterior domains.
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Report
(4 results)
Research Products
(5 results)