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

2007/08/31 by Martin Hadac, Sebastian Herr, Herbert Koch · 11 citations
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.1016/j.anihpc.2008.04.002

published as Ann. I. H. Poincare - AN (2009), Vol. 26, No. 3, pp. 917-941; Erratum: Ann. I. H. Poincare - AN (2010), Vol. 27, No. 3, pp. 971-972 · 28 pages; v3: erratum included

openalex publication_date 2008/05/08 · arxiv created 2009/12/23 · arxiv updated 2010/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

Abstract

The Cauchy problem for the Kadomtsev–Petviashvili-II equation (u_t + u_xxx + uu_x)_x + u_yy = 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.

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