On the growth of Sobolev norms for NLS on 2- and 3-dimensional manifolds
On the growth of Sobolev norms for NLS on 2- and 3-dimensional manifolds
Using suitable modified energies, we study higher-order Sobolev norms' growth in time for the nonlinear Schrödinger equation (NLS) on a generic 2-or 3-dimensional compact manifold.In two dimensions, we extend earlier results that dealt only with cubic nonlinearities, and get polynomial-in-time bounds for any higher-order nonlinearities.In three dimensions, we prove that …