Strichartz Estimates for Wave equations with Charge Transfer Hamiltonian

Abstract

We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in ${\mathbb{R}}^3$: \[ \partial_{tt}u-Δu+\sum_{j=1}^{m}V_{j}\left(x-\vec{v}_{j}t\right)u=0. \] 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.

72 pages

References in corpus (4)

• Fine properties of Charge Transfer Models
• Multisolitons for the defocusing energy critical wave equation with potentials
• Generic and non-generic behavior of solutions to the defocusing energy critical wave equation with potential in the radial case
• Wave equations with moving potentials

Cited by in corpus (4)

• Multisolitons for the defocusing energy critical wave equation with potentials
• Wave equations with moving potentials
• Strichartz estimates for the Klein--Gordon equation in ${\mathbb{R}}^{3+1}$
• L^p Boundedness of the Scattering Wave Operators of Schroedinger Dynamics with Time-dependent Potentials and applications