Mathematics > Analysis of PDEs
[Submitted on 9 Apr 2014 (v1), last revised 19 Mar 2017 (this version, v3)]
Title:On sharp bilinear Strichartz estimates of Ozawa-Tsutsumi type
View PDFAbstract:We provide a comprehensive analysis of sharp bilinear estimates of Ozawa-Tsutsumi type for solutions u of the free Schrödinger equation, which give sharp control on $|u|^2$ in classical Sobolev spaces. In particular, we provide a generalization of their estimates in such a way that provides a unification with some sharp bilinear estimates proved by Carneiro and Planchon-Vega, via entirely different methods, by seeing them all as special cases of a one parameter family of sharp estimates. We show that the extremal functions are solutions of the Maxwell-Boltzmann functional equation and provide a new proof that this equation admits only Gaussian solutions. We also make a connection to certain sharp estimates on $u^2$ involving certain dispersive Sobolev norms.
Submission history
From: Chris Jeavons [view email][v1] Wed, 9 Apr 2014 12:48:52 UTC (21 KB)
[v2] Mon, 1 Jun 2015 18:02:46 UTC (16 KB)
[v3] Sun, 19 Mar 2017 10:00:38 UTC (16 KB)
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