Some results on scattering for log-subcritical and log-supercritical nonlinear wave equations

研究成果: Article同行評審

3 引文 斯高帕斯(Scopus)

摘要

We consider two problems in the asymptotic behavior of semilinear second order wave equations. First, we consider the Ḣ1x × L2x scattering theory for the energy log-subcritical wave equation u= |u|4ug(|u|) in R1+3, where g has logarithmic growth at 0. We discuss the solution with general (respectively spherically symmetric) initial data in the logarithmically weighted (respectively lower regularity) Sobolev space. We also include some observation about scattering in the energy subcritical case. The second problem studied involves the energy log-supercritical wave equation u = |u|4u logα(2+|u|2) for 0 < α ≤ 43 in R1+3. We prove the same results of global existence and (Ḣ1x) Ḣ1x)× H1x scattering for this equation with a slightly higher power of the logarithm factor in the nonlinearity than that allowed in previous work by Tao.

原文English
頁(從 - 到)1-24
頁數24
期刊Analysis and PDE
6
發行號1
DOIs
出版狀態Published - 2013 八月 27

All Science Journal Classification (ASJC) codes

  • Analysis
  • Numerical Analysis
  • Applied Mathematics

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