| We consider the initial value problem for the defocusing energy-critical nonlinear Schrodinger equation in RxRn , n ≥ 5, * iut+Du=&vbm0;u&vbm0; 4n-2uu 0,x=u0 x, .;where the initial data u0 is chosen to belong to the energy-space H˙1( Rn ), and u(t, x) is a complex-valued function in spacetime RtxRn x .;We use the induction on energy technique introduced by J. Bourgain and extend the frequency-localized interaction Morawetz inequality introduced by J. Colliander, M. Keel, G. Staffilani, H. Takaoka, and T. Tao in dimension n = 3 to higher dimensions.;The results obtained are global well-posedness, scattering, and global L2n+2 n-2t,x spacetime bounds for solutions to the initial value problem (*). |
