EXISTENCE OF WEAK SOLUTIONS FOR A QUASILINEAR VERSION OF BENNEY EQUATIONS

Abstract

Benney introduced a general strategy for deriving systems of nonlinear partial differential equations associated with long- and short-wave solutions. The semi-linear Benney system was studied recently by Tsutsumi and Hatano. Here, we tackle the nonlinear version of it and using compensated compactness techniques, we prove the global existence of weak solutions to the Cauchy problem, in the case that the equation for the amplitude of the long wave is a quasilinear conservation law with flux f(v) = av 2 - bv 3 where a, b are constants with b > 0.