Unconditional uniqueness for the modified Korteweg–de Vries equation on the line
| Autor: | Luc Molinet, Stéphane Vento, Didier Pilod |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
General Mathematics
010102 general mathematics Mathematics::Analysis of PDEs 01 natural sciences 010101 applied mathematics Nonlinear Sciences::Exactly Solvable and Integrable Systems Line (geometry) Energy method A priori and a posteriori Applied mathematics Uniqueness 0101 mathematics Korteweg–de Vries equation Nonlinear Sciences::Pattern Formation and Solitons Energy (signal processing) Well posedness Mathematics |
| Zdroj: | Revista Matemática Iberoamericana. 34:1563-1608 |
| ISSN: | 0213-2230 |
| DOI: | 10.4171/rmi/1036 |
| Popis: | We prove that the modified Korteweg–de Vries (mKdV) equation is unconditionally well-posed in Hs(R) for s>1/3. Our method of proof combines the improvement of the energy method introduced recently by the first and third authors with the construction of a modified energy. Our approach also yields a priori estimates for the solutions of mKdV in Hs(R), for s>0, and enables us to construct weak solutions at this level of regularity. |
| Databáze: | OpenAIRE |
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