Small-data scattering for nonlinear waves with potential and initial data of critical decay

2005/03/11 by Paschalis Karageorgis, Karageorgis, Paschalis
Mathematics · #35B40 #35L05 #35L15 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B40 #msc:35L05 #msc:35L15

paper · pdf · doi:10.48550/arxiv.math/0503208

20 pages

arxiv created 2005/03/11 · arxiv updated 2009/12/01

Abstract

We study the scattering problem for the nonlinear wave equation with potential. In the absence of the potential, one has sharp existence results for the Cauchy problem with small initial data; those require the data to decay at a rate greater than or equal to a critical decay rate which depends on the order of the nonlinearity. However, scattering results have appeared only for the supercritical case. In this paper, we extend the scattering results to the critical case and we also allow the presence of a short-range potential.

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