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 $${\partial }_{t}u-{\partial }_x^{5}u-30u^2{\partial }_{x}u+20{\partial }_{x}u{\partial }_x^{2}u+10u{\partial }_x^{3}u=0.$$ 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.

36 pages

References in corpus (1)

• Nonlinear wave interactions for the Benjamin-Ono equation