Strichartz estimates for Schrödinger equations in weighted L² spaces and their applications

2015/03/14 by Youngwoo Koh, Koh, Youngwoo, Ihyeok Seo +1
Mathematics · #Advanced Mathematical Physics Problems #Mathematical Analysis and Transform Methods #Advanced Harmonic Analysis Research

paper · pdf · doi:10.48550/arxiv.1503.04268

Abstract

We obtain weighted L² Strichartz estimates for Schrödinger equations i∂_tu+(-Δ)^a/2u=F(x,t), u(x,0)=f(x), of general orders a>1 with radial data f,F with respect to the spatial variable x, whenever the weight is in a Morrey-Campanato type class. This is done by making use of a useful property of maximal functions of the weights together with frequency-localized estimates which follow from using bilinear interpolation and some estimates of Bessel functions. As consequences, we give an affirmative answer to a question posed in \citeBBCRV concerning weighted homogeneous Strichartz estimates, and improve previously known Morawetz estimates. We also apply the weighted L² estimates to the well-posedness theory for the Schrödinger equations with time-dependent potentials in the class.

Citations

• Improved Strichartz estimates for a class of dispersive equations in the radial case and their applications to nonlinear Schrödinger and wave equations

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