Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary

Details Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary

2010-04-22

arxiv.org/abs/1004.3976v2

Mathematics

Analysis of PDEs

Title change, and to appear in Math Annalen

Scientific paper

We establish Strichartz estimates for the Schr\"odinger equation on Riemannian manifolds $(\Omega,\g)$ with boundary, for both the compact case and the case that $\Omega$ is the exterior of a smooth, non-trapping obstacle in Euclidean space. The estimates for exterior domains are scale invariant; the range of Lebesgue exponents $(p,q)$ for which we obtain these estimates is smaller than the range known for Euclidean space, but includes the key $L^4_tL^\infty_x$ estimate, which we use to give a simple proof of well-posedness results for the energy critical Schr\"odinger equation in 3 dimensions. Our estimates on compact manifolds involve a loss of derivatives with respect to the scale invariant index. We use these to establish well-posedness for finite energy data of certain semilinear Schr\"odinger equations on general compact manifolds with boundary.

Affiliated with

Also associated with

No associations

Rating

Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Strichartz estimates and the nonlinear Schrödinger equation on manifolds with boundary will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-460084