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2017 Time-weighted estimates in Lorentz spaces and self-similarity for wave equations with singular potentials
Marcelo F. de Almeida, Lucas C. F. Ferreira
Anal. PDE 10(2): 423-438 (2017). DOI: 10.2140/apde.2017.10.423

Abstract

We show time-weighted estimates in Lorentz spaces for the linear wave equation with singular potential. As a consequence, assuming radial symmetry on initial data and potentials, we obtain well-posedness of global solutions in critical weak-Lp spaces for semilinear wave equations. In particular, we can consider the Hardy potential V (x) = c|x|2 for small |c|. Self-similar solutions are obtained for potentials and initial data with the right homogeneity. Our approach relies on performing estimates in the predual of weak-Lp, i.e., the Lorentz space L(p,1) .

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Marcelo F. de Almeida. Lucas C. F. Ferreira. "Time-weighted estimates in Lorentz spaces and self-similarity for wave equations with singular potentials." Anal. PDE 10 (2) 423 - 438, 2017. https://doi.org/10.2140/apde.2017.10.423

Information

Received: 2 July 2016; Accepted: 12 November 2016; Published: 2017
First available in Project Euclid: 16 November 2017

zbMATH: 1361.35037
MathSciNet: MR3619876
Digital Object Identifier: 10.2140/apde.2017.10.423

Subjects:
Primary: 35A01 , 35B06 , 35L05 , 35L15 , 35L71
Secondary: 35C06 , 42B35

Keywords: Lorentz spaces , radial symmetry , self-similarity , singular potentials , wave equations

Rights: Copyright © 2017 Mathematical Sciences Publishers

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