The authors establish microlocalized pointwise decay and Strichartz estimates for electromagnetic wave equations on n-dimensional product cones, with the admissible p-range restricted by the smallest eigenvalue of the angular operator.
Decay estimates for Schr\"{o}dinger's equation with magnetic potentials in three dimensions
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In this paper we prove that Schr\"{o}dinger's equation with a Hamiltonian of the form $H=-\Delta+i(A \nabla + \nabla A) + V$, which includes a magnetic potential $A$, has the same dispersive and solution decay properties as the free Schr\"{o}dinger equation. In particular, we prove $L^1 \to L^\infty$ decay and some related estimates for the wave equation. The potentials $A$ and $V$ are short-range and $A$ has four derivatives, but they can be arbitrarily large. All results hold in three space dimensions.
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Decay and Strichartz estimates for critical electromagnetic wave equations on conic manifolds
The authors establish microlocalized pointwise decay and Strichartz estimates for electromagnetic wave equations on n-dimensional product cones, with the admissible p-range restricted by the smallest eigenvalue of the angular operator.