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• W2963264823 abstract "We study the Cauchy problem for the one-dimensional wave equation $[ partial_t^2 u(t,x)-partial_x^2 u(t,x)+V(x)u(t,x)=0. ]$ The potential $V$ is assumed to be smooth with asymptotic behavior $[ V(x)sim -tfrac14 |x|^{-2}mbox{ as } |x|to infty. ]$ We derive dispersive estimates, energy estimates, and estimates involving the scaling vector field $tpartial_t+xpartial_x$, where the latter are obtained by employing a vector field method on the ``distorted'' Fourier side. Our results have immediate applications in the context of geometric evolution problems. The theory developed in this paper is fundamental for the proof of the co-dimension 1 stability of the catenoid under the vanishing mean curvature flow in Minkowski space, see Donninger, Krieger, Szeftel, and Wong, Codimension one stability of the catenoid under the vanishing mean curvature flow in Minkowski space" @default.
• W2963264823 created "2019-07-30" @default.
• W2963264823 creator A5044163410 @default.
• W2963264823 creator A5080736520 @default.
• W2963264823 date "2016-04-30" @default.
• W2963264823 modified "2023-10-01" @default.
• W2963264823 title "A Vector Field Method on the Distorted Fourier Side and Decay for Wave Equations With Potentials" @default.
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• W2963264823 hasPublicationYear "2016" @default.
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