A Geometric Proof of the Quasi-Linearity of the Water Waves System

In the first part of this paper we prove that flow associated to Burgers equation with a nonlocal term form fails be uniformly continuous from bounded sets for , and is Hilbert transform. Furthermore show cannot . We generalize result large class nonlinear transport-dispersive equations in any dimension, which particular contains Whitham paralinearization water waves system without surface tension. The current optimal sense Benjamin–Ono Lipschitz on function mean value second apply method deduce quasi-linearity system, main paper.