On the radius of spatial analyticity for Ostrovsky equation with positive dispersion

ABSTRACT

It is shown that the uniform radius of spatial analyticity $\sigma (t)$ of solutions at time t to the Ostrovsky equation with positive dispersion cannot decay faster than $|t{|}^{-\frac{4}{3}}$ as $|t|\to \mathrm{\infty }$ given initial data that is analytic with fixed radius ${\sigma }_0$. The main ingredients in the proof are almost conservation law for the solution to the Ostrovsky equation in space of analytic functions and space-time dyadic bilinear estimates associated with the Ostrovsky equation.

KEYWORDS:

• Ostrovsky equation with positive dispersion
• radius of spatial analyticity
• Gevrey spaces

AMS CLASSIFICATIONS:

• 35A20
• 35Q53
• 42B35

Disclosure statement

No potential conflict of interest was reported by the author(s).