Local well‐posedness of critical nonlinear Schrödinger equation on Zoll manifolds of odd‐growth

Abstract

In this paper, we study the nonlinear Schrödinger equation on Zoll manifolds with odd order nonlinearities. We will obtain the local well‐poesdness in the critical space . This extends the recent results in the literature to the Zoll manifolds of dimension d≥2 with general odd order nonlinearities and also partially improves the previous results in the subcritical spaces of Yang to the critical cases. Copyright © 2015 John Wiley & Sons, Ltd.