Vol. 3, No. 1, 2021

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Growth of Sobolev norms for coupled lowest Landau level equations

Valentin Schwinte and Laurent Thomann

Vol. 3 (2021), No. 1, 189–222
Abstract

We study coupled systems of nonlinear lowest Landau level equations, for which we prove global existence results with polynomial bounds on the possible growth of Sobolev norms of the solutions. We also exhibit explicit unbounded trajectories, which show that these bounds are optimal.

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Keywords
nonlinear Schrödinger equation, lowest Landau level, stationary solutions, progressive waves, solitons, growth of Sobolev norms
Mathematical Subject Classification
Primary: 35B08, 35C07, 35Q55, 37K06
Milestones
Received: 29 May 2020
Accepted: 24 January 2021
Published: 28 May 2021
Authors
Valentin Schwinte
Mines Nancy
Université de Lorraine
Nancy
France
Laurent Thomann
Institut Élie Cartan
Université de Lorraine
Nancy
France