Solvability of nonlinear dispersive equations with complicated resonance structure
Description: For the Cauchy problem of system of nonlinear Schrodinger equations, we almost completely characterized the Sobolev indexes which allows the well-posedness by the conditions focused on resonance structure. We also considered the Cauchy problem of nonlinear fourth order Schrodinger equations which have the polynomial nonlinearity with third order or lower spatial derivatives. We obtained the results for the well-posedness of this problem, which contain the improvement of the previous works. In particular, for the case that the equation has scale invariance, we obtained the well-posedness in the scaling critical Sobolev spaces. Furthermore, we clarified that the structure of Zakharov-Kuznetsov-Burgers equation, which is one of dispersive-dissipative model, is better than the structure of Zakharov-Kuznetsov equation, which has dispersion but not dissipation. To obtain this result, we prove the well-posedness of the Cauchy problem of Zakharov-Kuznetsov-Burgers equation.
Amount: ¥3,120,000
Funding type: fellowship
Funder scheme: Grant-in-Aid for Young Scientists (B)
Start date: 2017-04-01
End date: 2023-03-31
Investigator: Hiroyuki Hirayama
Institution: University of Miyazaki
Funded outputs count: 10
Funder award ID: 17K14220
OpenAlex ID: G2377166325