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. 1773–1826DOI 10.1016/J.ANIHPC.2018.03.002