| Budget Amount *help |
¥4,290,000 (Direct Cost: ¥3,300,000、Indirect Cost: ¥990,000)
Fiscal Year 2020: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2017: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
The author investigated Navier-Stokes equations, which describe motion of incompressible fluids, in 2-dimensional unbouded domains. (In particular exterior Gdomains.)
The author first considered stationary problem in exterior domains. No genaral condition was obtained for the existence of solutions which decay at infinity. The author showed the unique existence of weak solutions satisfying energy inequality under the assumption under newly introduced symmetry assumptions on domains, external forces and the boundary conditions.
The author next considered on the whole plane in the case where external forces depends on time. Under the aforementioned symmetry condition on the external forces, the author showed the unique existence and stability of small solutions. in oreder to overcome the weak decay in 2-dimension, we employed the weighted Lorentz spaces.
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