| Co-Investigator(Kenkyū-buntansha) |
TAKAGI Izumi Tohoku University, Graduate School of Science, Professor (40154744)
YANAGIDA Eiji Tohoku University, Graduate School of Science, Professor (80174548)
OGAWA Takayoshi Tohoku University, Graduate School of Science, Professor (20224107)
YANAGISAWA Taku Nara Women's University, Faculty of Science, Associate Professor (30192389)
NAKAMURA Makoto Tohoku University, Graduate School of Science, Associate Professor (70312634)
石毛 和弘 東北大学, 大学院・理学研究科, 助教授 (90272020)
松村 昭孝 大阪大学, 大学院・情報科学研究科, 教授 (60115938)
林 仲夫 大阪大学, 大学院・理学研究科, 教授 (30173016)
堤 誉志雄 東北大学, 大学院・理学研究科, 教授 (10180027)
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| Budget Amount *help |
¥79,300,000 (Direct Cost: ¥61,000,000、Indirect Cost: ¥18,300,000)
Fiscal Year 2007: ¥17,550,000 (Direct Cost: ¥13,500,000、Indirect Cost: ¥4,050,000)
Fiscal Year 2006: ¥14,040,000 (Direct Cost: ¥10,800,000、Indirect Cost: ¥3,240,000)
Fiscal Year 2005: ¥14,040,000 (Direct Cost: ¥10,800,000、Indirect Cost: ¥3,240,000)
Fiscal Year 2004: ¥14,950,000 (Direct Cost: ¥11,500,000、Indirect Cost: ¥3,450,000)
Fiscal Year 2003: ¥18,720,000 (Direct Cost: ¥14,400,000、Indirect Cost: ¥4,320,000)
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| Research Abstract |
1. Constructions of very weak solutions of the Navier-Stokes equations in exterior domains.
We show the unique existence of local very weak solutions to the prescribed non-homogeneous boundary data which belong to the larger class than the usual trace class. Our solutions satisfy the Serrin condition which implies the scaling invariant class.
2. New regularity criterion on weak solutions of the Navier-Stokes equations.
We prove that every turbulent solution which is α-Hoelder continuous in the kinetic energy in the time interval with α>1/2 necessarily regular.
3. Helmholtz-Weyl de composition in unbounded domains with non-compact boundaries of uniformly C^2-class.
Despite of a counter example of valiclity of the Helmholtz-Weyl decomposition in L^r, we introduce the space of sum and intersection of L^r and prove the Helmholtz-Weyl decomposition in such spaces. As an application, we can define the Stokes operator.
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