Propagation of Regularity and Persistence of Decay for Fifth Order Dispersive Models

Abstract

This paper considers the initial value problem for a class of fifth order dispersive models containing the fifth order KdV equation $$\begin{aligned} \partial _tu - \partial _x^5u -30u^2\partial _xu + 20\partial _xu\partial _x^2u + 10u\partial _x^3u = 0. \end{aligned}$$ The main results show that regularity or polynomial decay of the data on the positive half-line yields regularity in the solution for positive times.