Growth of Sobolev norms for linear Schrödinger operators
Thomann, Laurent1
1 Institut Élie Cartan, Université de Lorraine, B.P. 70239, F-54506 Vandœuvre-lès-Nancy Cedex, (France)
Annales Henri Lebesgue, Volume 4 (2021), pp. 1595-1618.

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.

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.

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DOI: 10.5802/ahl.111
Classification: 35Q41, 35B08
Mots-clés : Linear Schrödinger equation, time-dependent potential, growth of Sobolev norms, reducibility.
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},
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Thomann, Laurent. Growth of Sobolev norms for linear Schrödinger operators. Annales Henri Lebesgue, Volume 4 (2021), pp. 1595-1618. doi : 10.5802/ahl.111. http://www.numdam.org/articles/10.5802/ahl.111/

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