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math.APApr 15, 2013
11
citations (OpenAlex)
authors
  • Roland Donninger
  • Anıl Zenginoğlu
institutions
  • California Institute of Technology
  • École Polytechnique Fédérale de Lausanne
arXiv abstractPDF
paper

Nondispersive decay for the cubic wave equation

arXiv:1304.4135 · doi:10.2140/apde.2014.7.461

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

References in corpus (7)

  • Hyperboloidal foliations and scri-fixing
  • Relaxation of wave maps exterior to a ball to harmonic maps for all data
  • Stable self-similar blowup in energy supercritical Yang-Mills theory
  • Stable blow up dynamics for energy supercritical wave equations
  • Non-dispersive vanishing and blow up at infinity for the energy critical nonlinear Schrödinger equation in R^3
  • Threshold phenomenon for the quintic wave equation in three dimensions
  • Characterization of large energy solutions of the equivariant wave map problem: II

Cited by in corpus (4)

  • On blowup in supercritical wave equations
  • A globally stable self-similar blowup profile in energy supercritical Yang-Mills theory
  • Co-dimension one stable blowup for the supercritical cubic wave equation
  • Hyperboloidal evolution and global dynamics for the focusing cubic wave equation
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