Speaker : Dr. Hsi-Wei Shih(University of Minnesota)
Title : Some results on scattering for log-subcritical and log-supercritical nonlinear wave equations
Time : 2012-07-19 (Thu) 16:00 - 17:00
Place : Seminar Room 722, Institute of Mathematics (NTU Campus)
Abstract: We consider two problems in the asymptotic behavior of semilinear second order wave equations. First, we consider the scattering theory for the energy log-subcritical wave equation u = u 4 u g u in , where has logarithmic growth at . We discuss the solution with general (resp. spherically symmetric) initial data in the logarithmically weighted (resp. lower regularity) Sobolev space. The second problem studied here involves the energy log-supercritical wave equation u = u 4 u l o g α 2 + u 2 , f o r 0 < α 4 3 in . We prove the same results of global existence and scattering for the equation with a slightly higher power of the logarithm factor in the nonlinearity than that allowed by the previous work of Tao.