# Heat-flow monotonicity of Strichartz norms

Authors
Type
Preprint
Publication Date
Sep 27, 2008
Submission Date
Sep 27, 2008
Source
arXiv
Most notably we prove that for $d=1,2$ the classical Strichartz norm $$\|e^{i s\Delta}f\|_{L^{2+4/d}_{s,x}(\mathbb{R}\times\mathbb{R}^d)}$$ associated to the free Schr\"{o}dinger equation is nondecreasing as the initial datum $f$ evolves under a certain quadratic heat-flow.