Regularity of Solution of the Schrödinger Equation on Symmetric Space

2024/11/09 by Kumar, Pratyoosh, Sajjan, Manali
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2411.06104

Abstract

In this article, we investigate the behavior of solutions \( u(x,t) \) to the fractional Schrödinger equation on rank symmetric spaces of non-compact type. We proved that as time \( t \) approaches 0, then u(x,t) converges pointwise almost everywhere to the initial radial data \( f \), provided that \( f ∈ H^s(\mathbbX) \) with \( s > (1)/(2) \). This result extends Sjölin's results in this setting.

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