On the nonlinear Dysthe equation

Abstract This work is dedicated to putting on a solid analytic ground the theory of local well-posedness for two dimensional Dysthe equation. equation can be derived from incompressible Navier–Stokes after performing an asymptotic expansion wavetrain modulation fourth order. Recently, this has been used numerically study rare phenomena large water bodies such as rogue waves. In order well-posedness, we use Strichartz, and improved smoothing maximal function estimates. We follow ideas pioneering Kenig, Ponce Vega, but since highly anisotropic, several technical challenges had resolved. conclude our by also presenting ill-posedness result.