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- W2963851997 abstract "We undertake a comprehensive study of the nonlinear Schrodinger equation where u(t, x) is a complex-valued function in spacetime , λ1 and λ2 are nonzero real constants, and . We address questions related to local and global well-posedness, finite time blowup, and asymptotic behaviour. Scattering is considered both in the energy space H 1(ℝ n ) and in the pseudoconformal space Σ := {f ∈ H 1(ℝ n ); xf ∈ L 2(ℝ n )}. Of particular interest is the case when both nonlinearities are defocusing and correspond to the -critical, respectively -critical NLS, that is, λ1, λ2 > 0 and , . The results at the endpoint are conditional on a conjectured global existence and spacetime estimate for the -critical nonlinear Schrodinger equation, which has been verified in dimensions n ≥ 2 for radial data in Tao et al. (Tao et al. to appear a,b) and Killip et al. (preprint). As an off-shoot of our analysis, we also obtain a new, simpler proof of scattering in for solutions to the nonlinear Schrodinger equation with , which was fi..." @default.
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- W2963851997 date "2005-11-04" @default.
- W2963851997 modified "2023-10-18" @default.
- W2963851997 title "The nonlinear Schrödinger equation with combined power-type nonlinearities" @default.
- W2963851997 hasPublicationYear "2005" @default.
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