Global well-posedness of partially periodic KP-I equation in the energy space and application
Tristan Robert
Université de Cergy-Pontoise, Laboratoire AGM, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France
![Global well-posedness of partially periodic KP-I equation in the energy space and application cover](/_next/image?url=https%3A%2F%2Fcontent.ems.press%2Fassets%2Fpublic%2Fimages%2Fserial-issues%2Fcover-aihpc-volume-35-issue-7.png&w=3840&q=90)
Abstract
In this article, we address the Cauchy problem for the KP-I equation
for functions periodic in . We prove global well-posedness of this problem for any data in the energy space . We then prove that the KdV line soliton, seen as a special solution of KP-I equation, is orbitally stable under this flow, as long as its speed is small enough.
Cite this article
Tristan Robert, Global well-posedness of partially periodic KP-I equation in the energy space and application. Ann. Inst. H. Poincaré Anal. Non Linéaire 35 (2018), no. 7, pp. 1773–1826
DOI 10.1016/J.ANIHPC.2018.03.002