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Right limits and reflectionless measures for CMV matrices. (English) Zbl 1188.35172

The paper derives from earlier works by J. Bourgain [J. Am. Math. Soc. 12, No. 1, 145–171 (1999; Zbl 0958.35126)] and T. Tao [New York J. Math. 11, 57–80 (2005; Zbl 1119.35092)], a global well-posedness of a critical (and energy-critical) nonlinear Schrödinger equation with radial initial data and no potential. Those results are reviewed and their proofs signifcantly simplified. The introduction of a quadratic potential is a subtle point and relies on refinements of the previous techniques. Main steps towards the global well-posedness result involve the perturbation lemma, fractional chain rule and a specific monotonicity formula named Morawetz inequality.

MSC:

35Q55 NLS equations (nonlinear Schrödinger equations)
35B33 Critical exponents in context of PDEs
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