Nonlinear Schrödinger equations on compact Zoll manifolds with odd growth

Abstract

We study nonlinear Schrodinger equations on Zoll manifolds with nonlinear growth of the odd order. It is proved that local uniform well-posedness are valid in the Hs-subcritical setting according to the scaling invariance, apart from the cubic growth in dimension two. This extends the results by Burq et al. (2005) to higher dimensions with general nonlinearities.