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Growth of Sobolev norms
for coupled lowest Landau level equations
Valentin Schwinte and Laurent Thomann |
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Vol. 3 (2021), No. 1, 189–222
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Abstract |
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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
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Mathematical Subject Classification
Primary: 35B08, 35C07, 35Q55, 37K06
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Milestones
Received: 29 May 2020
Accepted: 24 January 2021
Published: 28 May 2021
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Authors |
| Valentin Schwinte | |
| Mines Nancy Université de Lorraine Nancy France |
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| Laurent Thomann | |
| Institut Élie Cartan Université de Lorraine Nancy France |
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