| Budget Amount *help |
¥5,200,000 (Direct Cost: ¥4,000,000、Indirect Cost: ¥1,200,000)
Fiscal Year 2015: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2014: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2013: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2012: ¥2,080,000 (Direct Cost: ¥1,600,000、Indirect Cost: ¥480,000)
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| Outline of Final Research Achievements |
The aims for our research are the following three studies: (1) Well-posedness and ill-posedness results for the Cauchy problem of some nonlinear wave euations. (2) The restriction theorems for the solutions for Schrodinger equations. (3) Hardy's inequalities, especially with the critical exponents.
For those aims, our results are the followings. (1) We studied the Cauchy problem for the Dirac-klein-Gordon equation, Chern-Simons-Dirac equation and the nonlinear half wave equations. We obtained some well-posed results and ill-posed results. Especially for Chern-Simons-Dirac equation, we succeed to define the class of well-posed or Ill-posed results in Sobolev spaces. (2) We found the class of extremizers for the trace theorem on the sphere. (3) We proved the Hardy inequality holds with some condition of index and fails with others.
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