Abstract
We study the well-posedness for the Cauchy problem of the KP II equation. We prove the local well-posedness in the anisotropic Sobolev spaces $H_{x,y}^{-1/4+\epsilon,0}$ and in the anisotropic homogeneous Sobolev spaces $H_{x,y}^{-1/2+4\epsilon,0}\cap\dot{H}_{x,y}^{-1/2+\epsilon,0}$. The first result is an improvement of the result in $L^2$ obtained by J. Bourgain [2].
Citation
Hideo Takaoka. "Well-posedness for the Kadomtsev-Petviashvili II equation." Adv. Differential Equations 5 (10-12) 1421 - 1443, 2000. https://doi.org/10.57262/ade/1356651228
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