Well-posedness of the initial value problem for the Korteweg-de Vries equation

Abstract

The conservation law ~k+2 ( .)provides an a priori estimate of the Hknorm (k = 0, 1, ... ) of a solution with data U o E Hk.Hence, combining the local result (s > 3/2), the invariants ~2 -~4' and some inequalities one obtains that the IVP (1.1) is globally well-posed in H S with s ~ 2 .