On the Benney]Lin and Kawahara Equations

We establish global well-posedness for the initial value problem IVP. associated to the so-called Benney]Lin equation. This model is a Korteweg]de Vries equation perturbed by dissipative and dispersive terms which appears in fluid dynamics. We also study the limiting behaviour of solutions to this IVP when the parameters of the perturbed terms approach 0.