On persistence of spatial analyticity for the dispersion-generalized periodic KdV equation

摘要

Persistence of spatial analyticity is studied for periodic solutions of the dispersion generalized KdV equation ut-vertical bar D-x vertical bar + uu(x) = 0 for alpha >= 2. For a class of analytic initial data with a uniform radius of analyticity sigma(0) > 0, we obtain an asymptotic lower bound sigma(t) >= ct(-p) on the uniform radius of analyticity sigma-(t) at time t, as t -> infinity, where p = max(1,4/alpha). The proof relies on bilinear estimates in Bourgain spaces and an approximate conservation law. (C) 2017 Elsevier Ltd. All rights reserved.