Growth of Sobolev norms for linear Schrödinger operators

Thomann, Laurent

doi:10.5802/ahl.111

Growth of Sobolev norms for linear Schrödinger operators
[Croissance de normes Sobolev pour des opérateurs Schrödinger linéaires]

Thomann, Laurent ¹

¹ Institut Élie Cartan, Université de Lorraine, B.P. 70239, F-54506 Vandœuvre-lès-Nancy Cedex, (France)

Annales Henri Lebesgue, Tome 4 (2021), pp. 1595-1618.

Résumé
Abstract

Nous donnons un exemple d’un opérateur de Schrödinger linéaire, dépendant du temps, avec une croissance optimale des normes de Sobolev. La construction est explicite, et s’appuie sur une étude complète de l’équation linéaire de plus bas niveau de Landau avec un potentiel dépendant du temps.

We give an example of a linear, time-dependent, Schrödinger operator with optimal growth of Sobolev norms. The construction is explicit, and relies on a comprehensive study of the linear Lowest Landau Level equation with a time-dependent potential.

Reçu le : 2020-06-02
Révisé le : 2021-02-25
Accepté le : 2021-04-14
Publié le : 2021-12-03

DOI : 10.5802/ahl.111

Classification : 35Q41, 35B08
Mots clés : Linear Schrödinger equation, time-dependent potential, growth of Sobolev norms, reducibility.

Affiliations des auteurs :

Thomann, Laurent ¹

¹ Institut Élie Cartan, Université de Lorraine, B.P. 70239, F-54506 Vandœuvre-lès-Nancy Cedex, (France)

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     title = {Growth of {Sobolev} norms for linear {Schr\"odinger} operators},
     journal = {Annales Henri Lebesgue},
     pages = {1595--1618},
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     volume = {4},
     year = {2021},
     doi = {10.5802/ahl.111},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/ahl.111/}
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Thomann, Laurent. Growth of Sobolev norms for linear Schrödinger operators. Annales Henri Lebesgue, Tome 4 (2021), pp. 1595-1618. doi : 10.5802/ahl.111. http://www.numdam.org/articles/10.5802/ahl.111/

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