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

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

2005-03-11

arxiv.org/abs/math/0503208v1

Mathematics

Analysis of PDEs

20 pages

Scientific paper

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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