Huaxiang Lu

The Wave Kinetic Theory for Quasilinear MMT Equation

We study the one-dimensional quasilinear Majda--McLaughlin--Tabak (MMT) equation on a large torus $[0,L]$: \begin{align*} i \partial_t u +2\pi|\nabla|^\sigma u +\lambda^{2}|\nabla|^\beta\left[ \left||\nabla|^\beta u\right|^{2} |\nabla|^\beta u\right]=0. \end{align*} Our focus is on the well-posedness of its dynamics an...