On the well-posedness for Kadomtsev-Petviashvili-Burgers I equation
Abstract
We prove local and global well-posedness in Hs,0(R2), s > -1/2, for the Cauchy problem associated with the Kadomotsev-Petviashvili-Burgers-I equation (KPBI) by working in Bourgain's type spaces. This result is almost sharp if one requires the flow-map to be smooth.
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