Growth of Sobolev norms for coupled Lowest Landau Level equations

TL;DR

This paper investigates coupled nonlinear lowest Landau level equations, establishing global existence with polynomial Sobolev norm growth bounds and demonstrating explicit solutions that reach these bounds, confirming their optimality.

Contribution

It provides the first proof of global existence with polynomial bounds for coupled lowest Landau level equations and constructs explicit solutions showing these bounds are sharp.

Findings

Global existence of solutions with polynomial Sobolev norm growth

Explicit unbounded trajectories matching the growth bounds

Optimality of the polynomial bounds on Sobolev norm growth

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.