Optimal bounds for the growth of Sobolev norms of solutions of a quadratic Szegő equation

Joseph Thirouin

In this paper, we study a quadratic equation on the one-dimensional torus : $$i{\partial }_{t}u=2J\Pi (|u{|}^2)+\bar{J}{u}^2,u(0,\cdot )=u_0,$$ where $J=\int_\mathbb{T}|u|^2u \in\ma…