Growth of Sobolev norms of solutions of linear Schrödinger equations on some compact manifolds

Jean-Marc Delort (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

We give a new proof of a theorem of Bourgain, asserting that solutions of linear Schrödinger equations on the torus, with smooth time dependent potential, have Sobolev norms growing at most like $t^\epsilon$ when $t\to +\infty$, for any $\epsilon>0$. Our proof extends to Schrödinger equations on other examples of compact riemannian manifolds.

Mots clés: Linear Schrödinger equation; Growth of solutions

Domaines: Equations aux dérivées partielles [math.AP]

Jean-Marc Delort. Growth of Sobolev norms of solutions of linear Schrödinger equations on some compact manifolds. 2009. ⟨hal-00389543v2⟩