Memoirs of the American Mathematical Society
1 total work
Strichartz Estimates for Wave Equations with Charge Transfer Hamiltonians
by Gong Chen
Published 1 May 2022
We prove Strichartz estimates (both regular and reversed) for a scattering state to the wave equation with a charge transfer Hamiltonian in R3:
?ttu ? ?u +m j=1 Vj (x ? vj t) 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 and local decay estimates. As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation. These estimates for this linear models are also of crucial importance for problems related to interactions of potentials and solitons, for example, in [GC4].
?ttu ? ?u +m j=1 Vj (x ? vj t) 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 and local decay estimates. As an application of our results, we show that scattering states indeed scatter to solutions to the free wave equation. These estimates for this linear models are also of crucial importance for problems related to interactions of potentials and solitons, for example, in [GC4].