| Budget Amount *help |
¥3,770,000 (Direct Cost: ¥2,900,000、Indirect Cost: ¥870,000)
Fiscal Year 2015: ¥780,000 (Direct Cost: ¥600,000、Indirect Cost: ¥180,000)
Fiscal Year 2014: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2013: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2012: ¥1,170,000 (Direct Cost: ¥900,000、Indirect Cost: ¥270,000)
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| Outline of Final Research Achievements |
The initial value problem for a fourth order dispersive partial differential equation for closed curve flow on a Kaehler manifold was mainly investigated.
The equation models the motion of a vortex filament or the continuum limit of a classical Heisenberg spin chain systems, where the manifold is the two-dimensional unit sphere. In our research, we investigated the relationship between the setting for the manifold and the structure of the equation, and applied the observation to the proof of the existence and the uniqueness of the solution. The main results is the time-local existence and the uniqueness of a smooth solution under the case where the manifold is a closed Riemann surface with constant curvature. Indeed, we found a nice solvable structure of the equation, and completed the proof by the mix of a suitable gauge transformation and the geometric energy method to eliminate the loss of derivatives.
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