Lower bound for the lifespan of solutions to the generalized KdV equation with low-degree of nonlinearity

Abstract

This paper is a survey article to review the Cauchy problem for the generalized KdV equation with low-degree of nonlinearity. In [5], the local well-posedness for the equation is established in an appropriate class under a non-degenerate condition for the initial data. In this paper, we give a lower bound estimate for the lifespan of the solution under the condition as a consequence of the contraction principle. The lifespan depends on the size and a quantity corresponding to the distance from zero of the initial data.