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	Normal form approach to global well-posedness of the quadratic derivative nonlinear Schrodinger equation on the circle
	Chung, Jaywan ; Guo, Zihua ; Kwon, Soonsik ; Oh, Tadahiro
	2017
关键词	Quadratic derivative nonlinear Schrodinger equation Normal form Cole-Hopf transform Fourier-Lebesgue space Well-posedness Finite time blowup BENJAMIN-ONO-EQUATION CAUCHY-PROBLEM
英文摘要	We consider the quadratic derivative nonlinear Schrodinger equation (dNLS) on the circle. In particular, we develop an infinite iteration scheme of normal form reductions for dNLS. By combining this normal form procedure with the Cole-Hopf transformation, we prove unconditional global well-posedness in L-2(T), and more generally in certain Fourier-Lebesgue spaces FLs,p (T), under the mean-zero and smallness assumptions. As a byproduct, we construct an infinite sequence of quantities that are invariant under the dynamics. We also show the necessity of the smallness assumption by explicitly constructing a finite time blowup solution with non-small mean-zero initial data. (C) 2016 Elsevier Masson SAS. All rights reserved.; NIMS grant - Korean Government [A23100000]; NRF of Korea [2015R1D1A1A01058832]; Posco Science Fellowship; European Research Council [637995]; SCI(E); ARTICLE; 5; 1273-1297; 34
语种	英语
出处	SCI
出版者	ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE
内容类型	其他
源URL	[http://hdl.handle.net/20.500.11897/471234]
专题	数学科学学院
推荐引用方式 GB/T 7714	Chung, Jaywan,Guo, Zihua,Kwon, Soonsik,et al. Normal form approach to global well-posedness of the quadratic derivative nonlinear Schrodinger equation on the circle. 2017-01-01.

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