Boa postura para alguns sistemas de equações dispersivas e para uma equação dispersiva

Abstract

The main aim of this work is to establish the well posedness for a dispersive partial differential equations systems and for a partial differential equation, with initial data belonging to Gevrey space. The proof relies on estimates in norms adapted to the linear part of the equations. In particular, estimates in Bourgain spaces are proven for the linear and nonlinear terms of the system and the main result is obtained by a contraction principle. The class of system in view contains a number of systems arising in the modeling of waves in fluids, stability and instability of solitary waves and models for wave propagation in physical systems where both nonlinear and dispersive effects are important. The techniques presented in this work were based in Grujić and Kalisch, see [21], who studied the well posedness of a IVP associated to a general equation, whose the initial data belongs to Gevrey spaces.