Nondispersive decay for the cubic wave equation

descriptionPublicationkeyboard_double_arrow_right Article , Preprint , Other literature type 30 May 2014Embargo end date: 01 Apr 2013 United States, Austria, Switzerland English Publisher:Mathematical Sciences PublishersJournal:Analysis & PDE, volume 7, pages 461-495 (issn: 2157-5045, eissn: 1948-206X,

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Authors: Donninger, Roland; ZenginoÄŸlu, AnÄ±l;

doi: 10.2140/apde.2014.7.461 , 10.48550/arxiv.1304.4135

arXiv: 1304.4135

handle: 20.500.14299/106151

Nondispersive decay for the cubic wave equation

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Abstract

We consider the hyperboloidal initial value problem for the cubic focusing wave equation. Without symmetry assumptions, we prove the existence of a co-dimension 4 Lipschitz manifold of initial data that lead to global solutions in forward time which do not scatter to free waves.

37 pages, 3 figures

Countries

United States, Austria, Switzerland

Related Organizations

École Polytechnique Fédérale de Lausanne EPFL
Switzerland
University of Vienna
Austria
California Institute of Technology
United States

Keywords

83C30, soliton resolution conjecture, FOS: Physical sciences, nonlinear wave equations, soliton resolution conjecture, hyperboloidal initial value problem, Kelvin coordinates, 101002 Analysis, General Relativity and Quantum Cosmology (gr-qc), RADIAL SOLUTIONS, 35L71, General Relativity and Quantum Cosmology, 510, 35L05, hyperboloidal initial value problem, Mathematics - Analysis of PDEs, FOS: Mathematics, 35L05, 35L71, 35Q75, 58J45, 83C30, Mathematical Physics, nonlinear wave equations, Soliton resolution conjecture, Hyperboloidal initial value problem, Mathematical Physics (math-ph), 58J45, 35Q75, BLOW-UP, SCATTERING-THEORY, GROUND-STATE, Nonlinear wave equations, Kelvin coordinates, GLOBAL DYNAMICS, Analysis of PDEs (math.AP)

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