Growth of Sobolev norms for coupled Lowest Landau Level equations

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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• Fermi-Pasta-Ulam phenomena and persistent breathers in the harmonic trap
• Logarithmic Schr{ö}dinger equation and isothermal fluids
• Growth of Sobolev Norms in 1-d Quantum Harmonic Oscillator with Polynomial Time Quasi-periodic Perturbation
• Almost reducibility and oscillatory growth of Sobolev norms
• Thomas-Fermi profile of a fast rotating Bose-Einstein condensate
• 1-d Quantum Harmonic Oscillator with Time Quasi-periodic Quadratic Perturbation: Reducibility and Growth of Sobolev Norms
• Energy cascades and condensation via coherent dynamics in Hamiltonian systems
• Reducibility of 1-D quantum harmonic oscillator with new unbounded oscillatory perturbations