O problema de Cauchy associado à equação KdV: uma abordagem sobre existência, unicidade e estabilidade de solução

Abstract

In this work, we study the existence, uniqueness and orbital stability of the Cauchy problem associated with the KdV equation. It is an exploratory study, based mainly on the theories of Tenenbaum and Pollard (1963) and Grillax, Shatah and Strauss (1987). The Korteweg-de Vries

Equation (KdV) stands out as one of the most important nonlinear dispersive differential equa- tions, being this a wave equation that generated so many other theories, it was the focus of our

studies with the intention of revisiting answers to the questions like: What does this equation models? Is the Cauchy Problem associated with it well posedness? Are your solutions orbitally stable? In this search, we understand that all these results are included and the methods used relate to other important equations. At the level of an undergraduate course, we highlight the presence of Conservation Laws such as energy and mass, and also the use of the Variational Calculus Theory, in a minimization problem to obtain orbital stability for their solutions.