#### Vol. 2, No. 2, 2009

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Heat-flow monotonicity of Strichartz norms

### Jonathan Bennett, Neal Bez, Anthony Carbery and Dirk Hundertmark

Vol. 2 (2009), No. 2, 147–158
##### Abstract

Our main result is that for $d=1,2$ the classical Strichartz norm $\parallel {e}^{is\Delta }f{\parallel }_{{L}_{s,x}^{2+4∕d}\left(ℝ×{ℝ}^{d}\right)}$ associated to the free Schrödinger equation is nondecreasing as the initial datum $f$ evolves under a certain quadratic heat flow.

##### Keywords
heat flow, Strichartz estimates, Schrödinger equation
##### Mathematical Subject Classification 2000
Primary: 35K05, 35Q40