Strichartz estimates for Schrödinger operators with a non-smooth magnetic potential

Abstract

We prove Strichartz estimates for the absolutely continuous evolution of a Schrödinger operator $H=(i\nabla +A{)}^2+V$ in ${\mathbb{R}}^n$, $n>2$. Both the magnetic and electric potentials are time-independent and satisfy pointwise polynomial decay bounds. The vector potential $A(x)$ is assumed to be continuous but need not possess any Sobolev regularity. This work is a refinement of previous methods, which required extra conditions on $\mathrm{div}A$ or $|\nabla {|}^{\frac{1}{2}}A$ in order to place the first order part of the perturbation within a suitable class of pseudo-differential operators.

12 pages

References in corpus (2)

• Strichartz and smoothing estimates for dispersive equations with magnetic potentials
• On global Strichartz estimates for non trapping metrics