The nonlinear Schrödinger equation with combined power-type nonlinearities Tao, Terence Visan, Monica Zhang, Xiaoyi Energy-critical Mass-critical Nonlinear Schrödinger equation Wellposedness We undertake a comprehensive study of the nonlinear Schrödinger equation (mathematical formular) where u(t, x) is a complex-valued function in spacetime R, xRn/x, λ1 and λ2 are nonzero real constants, and (mathematical formular). 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 L2/x-critical, respectively H1/x-critical NLS, that is, λ1, λ2 > 0 and (mathematical formular) . The results at the endpoint p1= 4/n are conditional on a conjectured global existence and spacetime estimate for the L2/x-critical nonlinear Schrödinger 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 H1/x for solutions to the nonlinear Schrödinger equation (mathematical formular) with 4/n < p < 4/n-2, which was first obtained by Ginibre and Velo (Citation1985). Informa UK Limited 2007 info:eu-repo/semantics/article doc-type:article text http://purl.org/coar/resource_type/c_2df8fbb1 https://research-explorer.ista.ac.at/record/22047 Tao T, Vişan M, Zhang X. The nonlinear Schrödinger equation with combined power-type nonlinearities. <i>Communications in Partial Differential Equations</i>. 2007;32(8):1281-1343. doi:<a href="https://doi.org/10.1080/03605300701588805">10.1080/03605300701588805</a> eng info:eu-repo/semantics/altIdentifier/doi/10.1080/03605300701588805 info:eu-repo/semantics/altIdentifier/issn/0360-5302 info:eu-repo/semantics/altIdentifier/e-issn/1532-4133 info:eu-repo/semantics/altIdentifier/arxiv/math/0511070 info:eu-repo/semantics/openAccess