A sharp regularity threshold for Schrödinger maximal estimates on standard tori

Xi Cen, Xitao Gao, Junyong Zhang

We disprove almost everywhere convergence of the Schrödinger evolution on the standard torus \(\mathbb{T}^d\) for initial data \(f\in H^s(\mathbb{T}^d)\) when \(s<d/(d+2)\), in all…