2014 Fiscal Year Final Research Report
New development of the theory on turbulence via method of nonlinear partial differential equations
Project/Area Number |
24654032
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Research Category |
Grant-in-Aid for Challenging Exploratory Research
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Allocation Type | Multi-year Fund |
Research Field |
Basic analysis
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Research Institution | Waseda University |
Principal Investigator |
KOZONO Hideo 早稲田大学, 理工学術院, 教授 (00195728)
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Co-Investigator(Kenkyū-buntansha) |
KANEDA Yukio 愛知工業大学, 工学部, 教授 (10107691)
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Project Period (FY) |
2012-04-01 – 2015-03-31
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Keywords | Navier-Stokes 方程式 / 外部問題の弱解の一意性 / 領域の位相幾何と可解性 / エネルギー不等式 / 指数安定性 |
Outline of Final Research Achievements |
To the 3D stationary Navier-Stokes equations in exterior domains, if the obstacle rotates slowly around the axis and moves also slowly along the same direction to the axis, then there exists a unique strong solution. In particular, we investigate the case when the obstacle moves with a constant speed and succeed to prove the energy inequality for any weak solution provided the external force is in the dual space of homogeneous Sobolev space with the first derivative in L^2. As an application, we can show the uniqueness of weak solutions under the smallness assumption on external forces. On the other hand, in the interior domain with multi-connected boundaries, if the inhomogeneous boundary data satisfies the Leray-Fujita inequality and if the stationary weak solution is close to the extended solenoidal vector field in L^3-norm, then it is asymptotically stable with an exponential convergence rate.
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Free Research Field |
非線形偏微分方程式
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