  This paper considers the initial value problem for a class of fifth order
dispersive models containing the fifth order KdV equation $$\partial_tu -
\partial_x^5u - 30u^2\partial_xu + 20\partial_xu\partial_x^2u +
10u\partial_x^3u = 0.$$ 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.
