Well-posedness of Cauchy problem of fractional drift diffusion system in non-critical spaces with power-law nonlinearity
| Autor: | Gu Caihong, Tang Yanbin |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2024 |
| Předmět: | |
| Zdroj: | Advances in Nonlinear Analysis, Vol 13, Iss 1, Pp 385-399 (2024) |
| Druh dokumentu: | article |
| ISSN: | 2191-950X 2024-0023 |
| DOI: | 10.1515/anona-2024-0023 |
| Popis: | In this article, we consider the global and local well-posedness of the mild solutions to the Cauchy problem of fractional drift diffusion system with higher-order nonlinearity. The main difficulty comes from the higher-order nonlinearity. Instead of the convention that people always focus on the properties of the solution in critical spaces, here we are interested in non-critical spaces such as supercritical Sobolev spaces and subcritical Lebesgue spaces. For the initial data in these non-critical spaces, using the properties of fractional heat semigroup and the classical Hardy-Littlewood-Sobolev inequality, we obtain the existence and uniqueness of the mild solution, together with the decaying rate estimates in terms of time variable. |
| Databáze: | Directory of Open Access Journals |
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