Seminar on Differential Equations

主講者: 史習偉博士 (University of Minnesota)
講題: Some results on scattering for log-subcritical and log-supercritical nonlinear wave equations
時間: 2012-07-19 (Thu.)  16:00 - 17:00
地點: 數學所 722 研討室 (台大院區)
Abstract: We consider two problems in the asymptotic behavior of semilinear second order wave equations. First, we consider the $\dot{H}^1_x\times L^2_x$ scattering theory for the energy log-subcritical wave equation u = u 4 u g u in $\mathbb{R}^{1+3}$, where $g$ has logarithmic growth at $0$. 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 $\mathbb{R}^{1+3}$. We prove the same results of global existence and $(\dot{H}^1_x\cap \dot{H}^2_x)\times H^1_x$ 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.
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