Sharp well-posedness for the Benjamin equation
نویسندگان
چکیده
منابع مشابه
Sharp ill-posedness result for the periodic Benjamin-Ono equation
We prove the discontinuity for the weak L(T)-topology of the flowmap associated with the periodic Benjamin-Ono equation. This ensures that this equation is ill-posed in Hs(T) as soon as s < 0 and thus completes exactly the well-posedness result obtained in [12]. AMS Subject Classification : 35B20, 35Q53.
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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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ژورنال
عنوان ژورنال: Nonlinear Analysis: Theory, Methods & Applications
سال: 2011
ISSN: 0362-546X
DOI: 10.1016/j.na.2011.06.002