Strichartz Estimates for Wave equations with Charge Transfer Hamiltonian

2016/10/17 by Chen, Gong · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.1610.05226

Abstract

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in ℝ³: ∂_ttu-Δu+∑_j=1^mV_j(x-v_jt)u=0. The energy estimate and the local energy decay of a scattering state are also established. In order to study nonlinear multisoltion systems, we will present the inhomogeneous generalizations of Strichartz estimates. As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation.

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• Scattering Theory and dispersive estimates for general 1d Charge Transfer Models

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