Heat-flow monotonicity of Strichartz norms

Abstract

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

11 pages