On the support of solutions to the Ostrovsky equation with positive dispersion

In this paper we prove that sufficiently smooth solutions of the Ostrovsky equation with positive dispersion, ∂tu+∂x3u+∂x−1u+u∂xu=0, that have exponential decay for x>0x>0 and such that their supports for two different times are contained in an interval (−∞,B](−∞,B], are identically zero.