| Budget Amount *help |
¥8,060,000 (Direct Cost: ¥6,200,000、Indirect Cost: ¥1,860,000)
Fiscal Year 2016: ¥1,690,000 (Direct Cost: ¥1,300,000、Indirect Cost: ¥390,000)
Fiscal Year 2015: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
Fiscal Year 2014: ¥1,820,000 (Direct Cost: ¥1,400,000、Indirect Cost: ¥420,000)
Fiscal Year 2013: ¥2,470,000 (Direct Cost: ¥1,900,000、Indirect Cost: ¥570,000)
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| Outline of Final Research Achievements |
The harmonic map heat flow equation and partial differential equations describing the incompressible fluids are studied. Concerning the harmonic map heat flow, we focused on equivariant maps from the n-dimensional Euclidean space to the n-dimensional sphere in energy supercritical dimensions and showed that certain data can give rise to two distinct solutions which are both stable. We also identified the optimal condition for the range of the solution to guarantee the uniqueness. In the research of the incompressible fluids, various results such as the Helmholtz decomposition and the structure theorem for the incompressible vector fields in unbounded domains are obtained.
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