Well-posedness results for the generalized Benjamin–Ono equation with small initial data
نویسندگان
چکیده
منابع مشابه
Sharp Well-posedness Results for the Generalized Benjamin-ono Equation with High Nonlinearity
We establish the local well-posedness of the generalized BenjaminOno equation ∂tu+H∂ xu±u ∂xu = 0 in Hs(R), s > 1/2−1/k for k ≥ 12 and without smallness assumption on the initial data. The condition s > 1/2−1/k is known to be sharp since the solution map u0 7→ u is not of class Ck+1 on Hs(R) for s < 1/2 − 1/k. On the other hand, in the particular case of the cubic Benjamin-Ono equation, we prov...
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Article history: Received 30 December 2014 Accepted 13 August 2015 Available online xxxx Communicated by Charles Fefferman MSC: 35R35 35Q35 35S10 76B03
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ژورنال
عنوان ژورنال: Journal de Mathématiques Pures et Appliquées
سال: 2004
ISSN: 0021-7824
DOI: 10.1016/j.matpur.2003.11.005