Hyperboloidal Evolution and Global Dynamics for the Focusing Cubic Wave Equation
 作者： Annegret Y. Burtscher,  Roland Donninger 作者单位： 1University of Bonn2University 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.

• 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