On growth of Sobolev norms for periodic nonlinear Schrödinger and generalised Korteweg-de Vries equations under critical Gibbs dynamics

Fabian Höfer, Niko A. Nikov

We prove logarithmic growth bounds on Sobolev norms of the focusing mass-critical NLS and gKdV equations on the torus, which hold almost surely under the focusing Gibbs measure wit…