WELL-POSEDNESS FOR THE SUPERCRITICAL GKDV EQUATION

In this paper we consider the supercritical generalized Korteweg-de Vries equation partial derivative t psi + partial derivative(xxx)psi+ partial derivative x(vertical bar psi vertical bar(p-1)psi) = 0, where 5 <= p is an element of R. We prove a local well-posedness result in the homogeneous Besov space B-infinity(s,p,2) (R), where s(p) = 1/2 - 2/p-1 is the scaling critical index. In particular local well-posedness in the smaller inhomogeneous Sobolev space H(s)p (R) can be proved similarly. As a byproduct a global well-posedness result for small initial data is also obtained.