no. 7
Global well-posedness of partially periodic KP-I equation in the energy space and application
Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 7, pp. 1773-1826.

In this article, we address the Cauchy problem for the KP-I equation

∂tu+∂x3u−∂x−1∂y2u+u∂xu=0
for functions periodic in y. We prove global well-posedness of this problem for any data in the energy space E={u∈L2(R×T),∂xu∈L2(R×T),∂x−1∂yu∈L2(R×T)}. 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.

DOI : 10.1016/j.anihpc.2018.03.002
Mots clés : Kadomtsev–Petviashvili equation, Global well-posedness, Orbital stability, KdV line soliton 
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Robert, Tristan. Global well-posedness of partially periodic KP-I equation in the energy space and application. Annales de l'I.H.P. Analyse non linéaire, Tome 35 (2018) no. 7, pp. 1773-1826. doi : 10.1016/j.anihpc.2018.03.002. http://www.numdam.org/articles/10.1016/j.anihpc.2018.03.002/

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