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• W2953052085 abstract "We consider the Cauchy problem for the nonlinear Schrodinger equations (NLS) with non-algebraic nonlinearities on the Euclidean space. In particular, we study the energy-critical NLS on $mathbb{R}^d$, $d=5,6$, and energy-critical NLS without gauge invariance and prove that they are almost surely locally well-posed with respect to randomized initial data below the energy space. We also study the long time behavior of solutions to these equations: (i) we prove almost sure global well-posedness of the (standard) energy-critical NLS on $mathbb{R}^d$, $d = 5, 6$, in the defocusing case, and (ii) we present a probabilistic construction of finite time blowup solutions to the energy-critical NLS without gauge invariance below the energy space." @default.
• W2953052085 created "2019-06-27" @default.
• W2953052085 creator A5028593330 @default.
• W2953052085 creator A5069067766 @default.
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• W2953052085 date "2017-08-04" @default.
• W2953052085 modified "2023-09-27" @default.
• W2953052085 title "On the probabilistic well-posedness of the nonlinear Schr{o}dinger equations with non-algebraic nonlinearities" @default.
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• W2953052085 hasPublicationYear "2017" @default.
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