Normal form approach to global well-posedness of the quadratic derivative nonlinear Schrodinger equation on the circle

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.
Publisher
ELSEVIER SCIENCE BV
Issue Date
2017-09
Language
English
Keywords

BENJAMIN-ONO-EQUATION; CAUCHY-PROBLEM

Citation

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, v.34, no.5, pp.1273 - 1297

ISSN
0294-1449
DOI
10.1016/j.anihpc.2016.10.003
URI
http://hdl.handle.net/10203/225804
Appears in Collection
MA-Journal Papers(저널논문)
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