| Budget Amount *help |
¥4,550,000 (Direct Cost: ¥3,500,000、Indirect Cost: ¥1,050,000)
Fiscal Year 2020: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥1,560,000 (Direct Cost: ¥1,200,000、Indirect Cost: ¥360,000)
Fiscal Year 2017: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
We studied the initial-boundary value problem and regularity of the solutions to
the incompressible Navier-Stokes equations. In particular, it was shown that there exist global in time weak solutions for the initial-boundary problem for the Navier-Stokes equations in the three dimensional half space for initial data with infinite energy. As for regularity of the solutions, we showed that if a scaled energy of the initial velocity is sufficiently small in some neighborhood, the weak solution is locally smooth at least for a short time. Furthermore, we obtained new estimates on regions where the weak solutions are smooth for initial data in the weighted spaces of square integrable functions.
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