Beckner, WilliamPavlovic, Natasa2011-10-252017-05-112011-10-252017-05-112011-08August 201http://hdl.handle.net/2152/ETD-UT-2011-08-4118textWe study the initial value problem for the defocusing nonlinear wave equation with cubic nonlinearity F(u)=|u|^2u in the energy-supercritical regime, that is dimensions d\geq 5. We prove that solutions to this equation satisfying an a priori bound in the critical homogeneous Sobolev space exist globally in time and scatter in the case of spatial dimensions d\geq 6 with general (possibly non-radial) initial data, and in the case of spatial dimension d=5 with radial initial data.application/pdfengGlobal well-posednessScatteringEnergy-supercriticalNonlinear wave equationthesis2011-10-252152/ETD-UT-2011-08-4118