DISCRETE SCHRODINGER EQUATION AND ILL-POSEDNESS FOR THE EULER EQUATION

被引：0
|
作者：
Jeong, In-Tee [1 ]
Pausader, Benoit [1 ]
机构：
[1] Kassar House,151 Thayer St, Providence, RI 02912 USA
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2017年 / 37卷 / 01期
基金：
美国国家科学基金会;
关键词：
The Euler equation; ill-posedness; norm inflation; discrete Schrodinger equation; Kolmogorov flow;
D O I：
10.3934/dcds.2017012
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the 2 D Euler equation with periodic boundary conditions in a family of Banach spaces based on the Fourier coefficients, and show that it is ill-posed in the sense that 'norm inflation' occurs. The proof is based on the observation that the evolution of certain perturbations of the 'Kolmogorov flow' given in velocity by U (x; y) = [GRAPHICS] can be well approximated by the linear Schrodinger equation, at least for a short period of time.
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页码：281 / 293
页数：13
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