2023/06/17 by Ghosh, Sunit, Mondal, Shyam Swarup, Swain, Jitendriya
#35J10 #35Q40 #35R03 #43A30 #43A80 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)
paper · doi:10.48550/arxiv.2306.10298
Let G=-Δ-|x|2∂t2 denote the Grushin operator on ℝn+1. The aim of this paper is two fold. In the first part, due to the non-dispersive phenomena of the Grushin-Schrödinger equation on ℝn+1, we establish a local dispersive estimate by defining the Grushin-Schrödinger kernel on a suitable domain. As a corollary we obtain a local Strichartz estimate for the Grushin-Schrödinger equation. In the next part, we prove a restriction theorem with respect to the scaled Hermite-Fourier transform on ℝn+2 for certain surfaces in ℕ0n×\mathbbR^*× ℝ and derive anisotropic Strichartz estimates for the Grushin-Schrödinger equation and for the Grushin wave equation as well.