Vol. 2, No. 2, 2009

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
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 eisΔfLs,x2+4 ∕ d(R×Rd) 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
Milestones
Received: 15 October 2008
Revised: 26 January 2009
Accepted: 24 March 2009
Published: 1 May 2009
Authors
Jonathan Bennett
School of Mathematics
The University of Birmingham
The Watson Building
Edgbaston
Birmingham, B15 2TT
United Kingdom
Neal Bez
Department of Mathematics
University Gardens
University of Glasgow, G12 8QW
United Kingdom
Anthony Carbery
School of Mathematics and Maxwell Institute for Mathematical Sciences
The University of Edinburgh
James Clerk Maxwell Building
The King’s Buildings
Edinburgh, EH3 9JZ
United Kingdom
Dirk Hundertmark
Department of Mathematics and Institute for Condensed Matter Theory
Altgeld Hall
University of Illinois at Urbana–Champaign
Urbana, IL 61801
United States