Well-posedness and scattering for the KP-II equation in a critical space

الأصل · EN

The Cauchy problem for the Kadomtsev-Petviashvili-II equation (uₜ+uxxx+uuₓ)ₓ+uyy=0 is considered. A small data global well-posedness and scattering result in the scale invariant, non-isotropic, homogeneous Sobolev space H⁻¹/²,⁰(R²) is derived. Additionally, it is proved that for arbitrarily large initial data the Cauchy problem is locally well-posed in the homogeneous space H⁻¹/²,⁰(R²) and in the inhomogeneous space H⁻¹/²,⁰(R²), respectively.