Pré-Publication, Document De Travail Année : 2009

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

Résumé

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.

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Dates et versions

hal-00389543 , version 1 (28-05-2009)
hal-00389543 , version 2 (07-01-2010)

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  • HAL Id : hal-00389543 , version 2

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