Strichartz estimates for Critical magnetic Schrödinger operators on flat Euclidean cones

In this paper, we study Schrödinger operator ${\mathcal{H}}_{\mathbf{A}}$ perturbed by critical magnetic potentials on the 2D flat cone $\mathrm{\Sigma }=C({\mathbb{S}}_{\rho }^1)=(0,\mathrm{\infty })\times {\mathbb{S}}_{\rho }^1$, which is a product cone over the circle ${\mathbb{S}}_{\rho }^1=\mathbb{R}\mathrm{/}2\pi \rho \mathbb{Z}$ with radius $\rho >0$, and equipped with the metric $g=d{r}^2+r^{2}d{\theta }^2$. The goal of this work is to establish Strichartz estimates for ${\mathcal{H}}_{\mathbf{A}}$ in this setting. A key aspect of our approach is the construction of the Schwartz kernel of the resolvent and the spectral measure for Schrödinger operator on the flat Euclidean cone $(\mathrm{\Sigma },g)$. The results presented here generalize previous work in \cite{Ford, BFM, FZZ, Zhang1}.