The Nonlinear Schrödinger Equation with Combined Power-Type Nonlinearities

  title={The Nonlinear Schr{\"o}dinger Equation with Combined Power-Type Nonlinearities},
  author={Terence Tao and Monica Visan and Xiaoyi Zhang},
  journal={Communications in Partial Differential Equations},
  pages={1281 - 1343}
We undertake a comprehensive study of the nonlinear Schrödinger 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… 
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