Hyperboloidal Evolution and Global Dynamics for the Focusing Cubic Wave Equation
作者: Annegret Y. BurtscherRoland Donninger
作者单位: 1University of Bonn
2University of Vienna
刊名: Communications in Mathematical Physics, 2017, Vol.353 (2), pp.549-596
来源数据库: Springer Nature Journal
DOI: 10.1007/s00220-017-2887-9
英文摘要: The focusing cubic wave equation in three spatial dimensions has the explicit solution \({\sqrt{2}/t}\) . We study the stability of the blowup described by this solution as \({t \to 0}\) without symmetry restrictions on the data. Via the conformal invariance of the equation we obtain a companion result for the stability of slow decay in the framework of a hyperboloidal initial value formulation. More precisely, we identify a codimension-1 Lipschitz manifold of initial data leading to solutions that converge to Lorentz boosts of \({\sqrt{2}/t}\) as \({t\to\infty}\) . These global solutions thus exhibit a slow nondispersive decay, in contrast to small data evolutions.
原始语种摘要: The focusing cubic wave equation in three spatial dimensions has the explicit solution \({\sqrt{2}/t}\) . We study the stability of the blowup described by this solution as \({t \to 0}\) without symmetry restrictions on the data. Via the conformal invariance of the equation we obtain a companion result for the stability of slow decay in the framework of a hyperboloidal initial value formulation. More precisely, we identify a codimension-1 Lipschitz manifold of initial data leading to solutions that converge to Lorentz boosts of \({\sqrt{2}/t}\) as \({t\to\infty}\) . These global solutions thus exhibit a slow nondispersive decay, in contrast to small data evolutions.
全文获取路径: Springer Nature  (合作)
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影响因子:1.971 (2012)

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关键词翻译
关键词翻译
  • hyperboloidal 双曲面的
  • symmetry 对称
  • focusing 
  • framework 构架
  • invariance 不变性
  • precisely 准确地
  • dimensions 面积
  • nondispersive 非分散的
  • stability 稳定性
  • spatial 空间的