Linear restriction estimates for Schroedinger equation on metric cones

الأصل · EN

In this paper, we study some modified linear restriction estimates of the dynamics generated by Schroedinger operator on metric cone M, where the metric cone M is of the form M=(0,∞)ᵣ×Σ with the cross section Σ being a compact (n-1)-dimensional Riemannian manifold (Σ,h) and the equipped metric is g=dr²+r²h. Assuming the initial data possesses additional regularity in angular variable θ∈Σ, we show some linear restriction estimates for the solutions. As applications, we obtain global-in-time Strichartz estimates for radial initial data and show small initial data scattering theory for the mass-critical nonlinear Schroedinger equation on two-dimensional metric cones.