Long time behavior of solutions of nonlinear dispersive equations

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I worked on several problems. I proved global existence and scattering of nonsmooth solutions of some barely supercritical Schrodinger equations with a defocusing (i.e repulsive) nonlinearity: this lead to a paper recently published in International Mathematics Research Notices. I also proved global existence and scattering of smooth and nonsmooth solutions below ground state of some size-dependent barely supercritical Schrodinger equations with a focusing (i.e attractive) nonlinearity: this lead to a preprint (arXiv:1701.02689). I also worked on a problem with Prof Kotaro Tsugawa (Nagoya University and Chuo University) that involves the construction of local smooth solutions of fully nonlinear equations that satisfya dispersive property in a weak sense. This collaboration is about to lead to a preprint.