Well-posedness and Ill-posedness Results for the Kadomtsev-petviashvili-i Equation
نویسنده
چکیده
The main results of this paper are concerned with the “bad” behavior of the KP-I equation with respect to a Picard iteration scheme applied to the associated integral equation, for data in usual or anisotropic Sobolev spaces. This leads to some kind of ill-posedness of the corresponding Cauchy problem: the flow map cannot be of class C2 in any Sobolev space.
منابع مشابه
Well-posedness of the Fifth Order Kadomtsev-Petviashvili I Equation in Anisotropic Sobolev Spaces with Nonnegative Indices
In this paper we establish the local and global well-posedness of the real valued fifth order Kadomstev-Petviashvili I equation in the anisotropic Sobolev spaces with nonnegative indices. In particular, our local well-posedness improves SautTzvetkov’s one and our global well-posedness gives an affirmative answer to SautTzvetkov’s L-data conjecture.
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