| Budget Amount *help |
¥2,730,000 (Direct Cost: ¥2,100,000、Indirect Cost: ¥630,000)
Fiscal Year 2016: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2015: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
I have studied regularity and asymptotic behavior of solutions for the Navier-Stokes equations, which describes the motion of viscous incompressible flows such as the atmosphere and the water. In this research project, I have worked on the two problems.
The first problem is an axisymmetric solution. I have constructed global unique axisymmetric solutions in an exterior domain subject to the slip boundary condition for decaying and sufficiently smooth initial data.
The second is a non-decaying solution. I have constructed local-in-time unique solutions in an exterior domain in a space of bounded functions. For the two-dimensional case, I have proved that global unique solutions exist for bounded initial data with a finite Dirichlet integral.
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