PUB - Publikationen an der Universität Bielefeld

Let (M, g) be a three-dimensional smooth compact Riemannian manifold such that all geodesics are simple and closed with a common minimal period, such as the 3-sphere S-3 with canonical metric. In this work the global well-posedness problem for the quintic nonlinear Schrodinger equation i partial derivative(t)u + Delta u = +/-vertical bar u vertical bar(4)u, u vertical bar(t=0) = u(0) is solved for small initial data u(0) in the energy space H-1(M), which is the scaling-critical space. Further, local well-posedness for large data, as well as persistence of higher initial Sobolev regularity is obtained. This extends previous results of Burq-Gerard-Tzvetkov to the endpoint case.