Global regularity for supercritical nonlinear dissipative wave equations in 3D

摘要

The nonlinear wave equation u(tt) - Delta u+vertical bar u(t)vertical bar(p-1)u(t) = 0 is shown to be globally well posed in the Sobolev spaces of radially symmetric functions H-rad(k)(R-3) x H-rad(k-1)(R-3) for all p >= 3 and k >= 3. Moreover, global C-infinity solutions are obtained when the initial data are C-0(infinity) and exponent p is an odd integer.