Nonlinear Schrödinger equation on four-dimensional compact manifolds

Details Nonlinear Schrödinger equation on four-dimensional compact manifolds Nonlinear Schrödinger equation on four-dimensional compact manifolds

2005-08-06

arxiv.org/abs/math/0508116v2

Mathematics

Analysis of PDEs

27 pages

Scientific paper

We prove two new results about the Cauchy problem for nonlinear Schroedinger equations on four-dimensional compact manifolds. The first one concerns global wellposedness for Hartree-type nonlinearities and includes approximations of cubic NLS on the sphere. The second one provides local wellposedness for quadratic nonlinearities in the case of zonal data on the sphere. Both results are based on new multilinear Strichartz-type estimates for the Schroedinger group.

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