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.Comment: 11 page

Bennett, Jonathan

Bez, Neal

Carbery, Anthony

Hundertmark, Dirk

English

arXiv

Our main result is that for d = 1, 2 the classical Strichartz norm parallel to e(is Delta) f parallel to(2+4/d)(Ls,x)(RxR(d)) associated to the free Schrodinger equation in nondecreasing as the initial datum f evolves under a certain quadratic heat flow

Bez, Richard

Carbery, A

Hundertmark, D

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