On the Non-Linear Schrodinger Equation on a Compact Manifold

Annie Millet (1, 2) , Zdzislaw Brzezniak (3)

1 SAMM - Statistique, Analyse et Modélisation Multidisciplinaire (SAmos-Marin Mersenne)
2 LPMA - Laboratoire de Probabilités et Modèles Aléatoires
3 University of York [York, UK]

We consider a non-linear Schrodinger equation on a compact manifold of dimension d subject to some multiplicative random perturbation. Using some stochastic Strichartz inequality, we prove the existence and uniqueness of a maximal solution in H1 under some general conditions on the diffusion coefficient. Under stronger conditions on the noise, the nonlinearity and the diffusion coefficient, we deduce the existence of a global solution when d=2. This is a joint work with Z. Brzezniak.

Mots clés: Schrödinger equation; compact manifold; Strichartz inequality; Stratonovich integral; global well posedeness

Domaines: Probabilités [math.PR]

Annie Millet, Zdzislaw Brzezniak. On the Non-Linear Schrodinger Equation on a Compact Manifold. International Conference on Malliavin Calculus and Stochastic Analysis in Honor of Professor David Nualart, Mar 2011, Lawrence (Kansas), United States. http://www.math.ku.edu/conferences/2011Malliavin/talks.html. ⟨hal-00624308⟩