Heat-flow monotonicity of Strichartz norms

Details Heat-flow monotonicity of Strichartz norms Heat-flow monotonicity of Strichartz norms

2008-09-27

arxiv.org/abs/0809.4783v1

Mathematics

Classical Analysis and ODEs

11 pages

Scientific paper

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.

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