The local well-posedness of the periodic Benjamin equation with small initial value in H s (T), s ≥ -1/2, is given. It is here shown that -1/2 is the lower endpoint to obtain the bilinear estimates which are the crucial steps to obtain the local well-posedness by the Picard iteration.
MSC: 35Q53; 35Q55
We study global well-posedness for the Kadomtsev-Petviashvili II equation in three space dimensions with small initial data. The crucial points are new bilinear estimates and the definition of the function spaces. As byproduct we obtain that all solutions to small initial data scatter as t → ±∞.
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