Local well-posedness for quasi-linear NLS with large Cauchy data on the circle

被引：20

作者：

Feola, R. ^{[1
]}

Iandoli, F. ^{[1
]}

机构：

[1] SISSA, Trieste, Italy

来源：

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE | 2019年 / 36卷 / 01期

关键词：

NLS; Quasi-linear PDEs; Para-differential calculus; Local wellposedness; Dispersive equations; Energy method; KAM; PERTURBATIONS; EQUATIONS;

D O I：

10.1016/j.anihpc.2018.04.003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove local in time well-posedness for a large class of quasilinear Hamiltonian, or parity preserving, Schrodinger equations on the circle. After a paralinearization of the equation, we perform several paradifferential changes of coordinates in order to transform the system into a paradifferential one with symbols which, at the positive order, are constant and purely imaginary. This allows to obtain a priori energy estimates on the Sobolev norms of the solutions. (C) 2018 Elsevier Masson SAS. All rights reserved.

引用

页码：119 / 164

页数：46

共 25 条

[1] Control of water waves [J].