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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.
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
