Strichartz estimates for the Schrödinger equation on products of odd-dimensional spheres

Abstract

We prove Strichartz estimates for the Schrödinger equation which are scale-invariant up to an $\epsilon$-loss on products of odd-dimensional spheres. Namely, for any product of odd-dimensional spheres $M={\mathbb{S}}^{d_1}\times \cdots \times {\mathbb{S}}^{d_r}$ (so that $M$ is of dimension $d=d_1+\cdots +d_r$ and rank $r$) equipped with rational metrics, the following Strichartz estimate \begin{equation*} \|e^{itΔ}f\|_{L^p(I\times M)}\leq C_\varepsilon\|f\|_{H^{\frac{d}{2}-\frac{d+2}{p}+\varepsilon}(M)} \end{equation*} holds for any $p\ge 2+\frac{8(s-1)}{sr}$, where $$s=\max \left\{\frac{2d_i}{d_i-1},i=1,\dots ,r\right\}.$$

arXiv commentThis paper is mainly the old published paper in Nonlinear Analysis. However, some arguments are slightly upgraded so that the results presented here are stronger and new

References in corpus (5)

• Nonlinear Schrödinger equation on real hyperbolic spaces
• The quintic nonlinear Schrödinger equation on three-dimensional Zoll manifolds
• On Fourier restriction type problems on compact Lie groups
• Strichartz estimates for the Schrödinger flow on compact Lie groups
• Sharp Strichartz estimates for the Schrödinger equation on the sphere

Cited by in corpus (1)

• Schrödinger equations on compact globally symmetric spaces