Heat-flow monotonicity of Strichartz norms

Abstract

Most notably we prove that for $d=1,2$ the classical Strichartz norm $$\|e^{i sΔ}f\|_{L^{2+4/d}_{s,x}(\mathbb{R}\times\mathbb{R}^d)}$$ associated to the free Schrödinger equation is nondecreasing as the initial datum $f$ evolves under a certain quadratic heat-flow.

11 pages