### Tristan Robert

Université de Cergy-Pontoise, Laboratoire AGM, 2 av. Adolphe Chauvin, 95302 Cergy-Pontoise Cedex, France

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

$∂_{t}u+∂_{x}u−∂_{x}∂_{y}u+u∂_{x}u=0$

for functions periodic in $y$. We prove global well-posedness of this problem for any data in the energy space $E={u∈L_{2}(R×T),∂_{x}u∈L_{2}(R×T),∂_{x}∂_{y}u∈L_{2}(R×T)}$. 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.

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