The quintic NLS on perturbations of R³

2016/07/13 by Casey Jao, Jao, Casey
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Black Holes and Theoretical Physics #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1607.03851

Abstract

Consider the defocusing quintic nonlinear Schrödinger equation on R³ with initial data in the energy space. This problem is "energy-critical" in view of a certain scale-invariance, which is a main source of difficulty in the analysis of this equation. It is a nontrivial fact that all finite-energy solutions scatter to linear solutions. We show that this remains true under small compact deformations of the Euclidean metric. Our main new ingredient is a long-time microlocal weak dispersive estimate that accounts for the refocusing of geodesics.

Citations

• A relation between pointwise convergence of functions and convergence of functionals

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