| Budget Amount *help |
¥4,680,000 (Direct Cost: ¥3,600,000、Indirect Cost: ¥1,080,000)
Fiscal Year 2020: ¥650,000 (Direct Cost: ¥500,000、Indirect Cost: ¥150,000)
Fiscal Year 2019: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2018: ¥1,300,000 (Direct Cost: ¥1,000,000、Indirect Cost: ¥300,000)
Fiscal Year 2017: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2016: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
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| Outline of Final Research Achievements |
We founded the weakest norm that satisfies the Brezis-Gallouet-Wainger type inequality, under some conditions. As an application of the Brezis-Gallouet-Wainger type inequality, we gave Beale-Kato-Majda type blow-up criteria of smooth solutions to the 3-D Navier-Stokes equations in unbounded domains. For example, we proved that, if [0,T) is the maximal interval of existence of a smooth solution u to the Navier-Stokes equations, then
int_(0,T) || rot u(s)||_{bmo}ds= infty.
Moreover, we improved this blow-up criterion by using a space of Morrey type.
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