Remarks on some dispersive estimates
type: Item
instance of: scholarly article
title: Remarks on some dispersive estimates
zbMATH Open document ID: 1232.35136
author: Yonggeun Cho
author: Tohru Ozawa
author: Suxia Xia
published in: Communications on Pure and Applied Analysis
publication date: 2011-12-19T00:00:00Z
review text: The authors derive dispersive estimates of the solution to the initial value problem to the general dispersive equation \[ i\partial_t u+\omega(|\nabla|)u=0 \;\text{ in } \mathbb R^{n+1}, \quad u(0)=\varphi \;\text{ in } \mathbb R^n, \] under suitable smoothness and growth conditions on \(\omega.\) They unify and simplify all the known dispersive estimates by utilizing the Bessel function and extend them to more general cases.
Mathematics Subject Classification ID: 35Q40
Mathematics Subject Classification ID: 42B37
zbMATH DE Number: 5989652
zbMATH Keywords: dispersive equations
zbMATH Keywords: dispersive estimate
zbMATH Keywords: oscillatory integral
zbMATH Keywords: time decay
zbMATH Keywords: Strichartz estimate
zbMATH Keywords: Bessel functions
reviewed by: Lubomira Softova
MaRDI profile type: Publication
full work available at URL: cpaa.2011.10.1121
OpenAlex ID: W2332945974
DOI: 10.3934/CPAA.2011.10.1121
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description: scientific article; zbMATH DE number 5989652