| Budget Amount *help |
¥3,900,000 (Direct Cost: ¥3,000,000、Indirect Cost: ¥900,000)
Fiscal Year 2021: ¥520,000 (Direct Cost: ¥400,000、Indirect Cost: ¥120,000)
Fiscal Year 2020: ¥910,000 (Direct Cost: ¥700,000、Indirect Cost: ¥210,000)
Fiscal Year 2019: ¥1,040,000 (Direct Cost: ¥800,000、Indirect Cost: ¥240,000)
Fiscal Year 2018: ¥1,430,000 (Direct Cost: ¥1,100,000、Indirect Cost: ¥330,000)
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| Outline of Final Research Achievements |
We considered the Cauchy problem of fifth order KdV type equations on the one-dimensional torus. We proved the well-posedness and unconditional uniqueness. This result is optimal in the sense that the nonlinear terms can be defined as the distribution. The key of this study is how to deal with the resonant parts which cannot be regarded as the perturbation of the linearized solution. By symmetry of the equation, we found that the resonant parts are exactly localized and can be cancelled by some conserved quantities.
Moreover, we obtained the improved results of fifth order modified KdV type equations and third order Benjamin-Ono type equations on the torus.
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