Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity

André de Laire (1)

1 LJLL - Laboratoire Jacques-Louis Lions

We study the Gross-Pitaevskii equation involving a nonlocal interaction potential. Our aim is to give sufficient conditions that cover a variety of nonlocal interactions such that the associated Cauchy problem is globally well-posed with non-zero boundary condition at infinity, in any dimension. We focus on even potentials that are positive definite or positive tempered distributions.

Mots clés: Nonlocal Schrodinger equation; Gross-Pitaevskii equation; Global ell-posedness; Initial value problem

Domaines: Equations aux dérivées partielles [math.AP]

André de Laire. Global well-posedness for a nonlocal Gross-Pitaevskii equation with non-zero condition at infinity. Communications in Partial Differential Equations, 2010, 35 (11), pp.2021-2058. ⟨10.1080/03605302.2010.497200⟩. ⟨hal-00593629⟩