Heat-flow monotonicity of Strichartz norms

Jonathan Bennett; Richard Bez; A Carbery; D Hundertmark

doi:10.2140/apde.2009.2.147

Heat-flow monotonicity of Strichartz norms

Jonathan Bennett, Richard Bez, A Carbery, D Hundertmark

Mathematics

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Abstract

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.

Original language	English
Pages (from-to)	147-158
Number of pages	12
Journal	Analysis and PDE
Volume	2
Issue number	2
DOIs	https://doi.org/10.2140/apde.2009.2.147
Publication status	Published - 1 Jan 2009

Keywords

Strichartz estimates
heat flow
Schrodinger equation

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10.2140/apde.2009.2.147

Strichartzmonotonicity PUREversionAccepted author manuscript, 219 KB

New Approaches to Central Problems in Euclidean Harmonic Analysis and Geometric Combinatorics
Bennett, J.
Engineering & Physical Science Research Council
3/01/07 → 2/01/10
Project: Research Councils

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title = "Heat-flow monotonicity of Strichartz norms",

abstract = "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.",

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author = "Jonathan Bennett and Richard Bez and A Carbery and D Hundertmark",

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AU - Bez, Richard

AU - Carbery, A

AU - Hundertmark, D

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N2 - 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.

AB - 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.

KW - Strichartz estimates

KW - heat flow

KW - Schrodinger equation

U2 - 10.2140/apde.2009.2.147

DO - 10.2140/apde.2009.2.147

M3 - Article

VL - 2

SP - 147

EP - 158

JO - Analysis and PDE

JF - Analysis and PDE

IS - 2

ER -

Heat-flow monotonicity of Strichartz norms

Abstract

Keywords

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New Approaches to Central Problems in Euclidean Harmonic Analysis and Geometric Combinatorics

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