{"id":"https://openalex.org/G2377166325","display_name":"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.","funder_award_id":"17K14220","funder":{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","doi":"10.13039/501100001691"},"funded_outputs":["https://openalex.org/W2901303794","https://openalex.org/W2962941535","https://openalex.org/W2963352510","https://openalex.org/W2975215898","https://openalex.org/W3127960817","https://openalex.org/W3167172920","https://openalex.org/W4285231123","https://openalex.org/W4379203666","https://openalex.org/W4392528749","https://openalex.org/W4396632209"],"funded_outputs_count":10,"parent_awards":[],"sub_awards":[],"sub_awards_count":0,"amount":3120000.0,"currency":"JPY","amount_usd":27901.23,"amount_usd_basis":"daily_rate","recipients":[],"recipient_countries":[],"recipient_regions":[],"research_scope":{"is_research":true,"basis":"funder_default","tier":1},"funding_type":"fellowship","funder_scheme":"Grant-in-Aid for Young Scientists (B)","start_date":"2017-04-01","end_date":"2023-03-31","start_year":2017,"end_year":2023,"landing_page_url":"https://kaken.nii.ac.jp/en/grant/KAKENHI-PROJECT-17K14220/","doi":null,"provenance":"kaken","lead_investigator":{"given_name":"Hiroyuki","family_name":"Hirayama","orcid":null,"role_start":null,"affiliation":{"name":"University of Miyazaki","country":"Japan","ids":[{"id":"https://nrid.nii.ac.jp/nrid/1000090748328","type":"nrid","asserted_by":"kaken"}]}},"co_lead_investigator":null,"investigators":null,"works_api_url":"https://api.openalex.org/works?filter=awards.id:G2377166325","primary_topic":null,"topics":null,"institution_awarded":[{"id":"https://openalex.org/I118574687","display_name":"University of Miyazaki","ror":"https://ror.org/0447kww10","country_code":"JP","type":"education","lineage":["https://openalex.org/I118574687"]}],"updated_date":"2026-10-16T03:01:01.000Z","created_date":"2026-07-13T04:17:19.000Z"}