컨텐츠 시작
학술대회/행사
초록검색
| 제출번호(No.) | 0124 |
|---|---|
| 분류(Section) | Special Session |
| 분과(Session) | (SS-08) Recent Trend in Fluid Equations (SS-08) |
| 발표시간(Time) | 20th-D-14:00 -- 14:20 |
| 영문제목 (Title(Eng.)) |
The global Cauhcy problem for the Euler-Riesz system |
| 저자(Author(s)) |
Young-Pil Choi1, Jinwook Jung2, Yoonjung Lee1 Yonsei University1, Hanyang University2 |
| 초록본문(Abstract) | We completely resolve the global Cauchy problem for the multi-dimensional Euler-Riesz equations, where the interaction forcing is given by $\nabla (-\Delta)^{-\sigma/2}\rho$ for some $\sigma \in (0,2)$. We construct the global-in-time unique solution to the Euler-Riesz system in a $H^s$ Sobolev space under a smallness assumption on the initial density and a {\it dispersive} spectral condition on the initial velocity. Moreover, we investigate the algebraic time decay of convergences for the constructed solutions. Our results cover both attractive and repulsive cases as well as the whole regime $\sigma \in (0,2)$. |
| 분류기호 (MSC number(s)) |
76N10 |
| 키워드(Keyword(s)) | Cauchy problem, Euler-Riesz system, temporal decay, global existence |
| 강연 형태 (Language of Session (Talk)) |
Korean |