负Sobolev空间二次非线性$$\overline{u}^2$$周期非线性Schrödinger方程的局部适定性

IF 1.4 4区数学 Q1 MATHEMATICS

Journal of Dynamics and Differential Equations Pub Date : 2025-01-01 Epub Date: 2023-08-07 DOI:10.1007/s10884-023-10295-x

Ruoyuan Liu

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引用次数: 0

摘要

研究了二阶非线性u¯2的非线性Schrödinger方程（NLS）在一维环面和二维环面上的低正则局部适定性。虽然已知当正则性s低于某个阈值时，关于X s， b -空间的相关双线性估计是失败的，但我们通过在X s， b -空间上引入修改，建立了这种低正则性的局部适定性。

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Local Well-Posedness of the Periodic Nonlinear Schrödinger Equation with a Quadratic Nonlinearity u ¯ 2 in Negative Sobolev Spaces.

We study low regularity local well-posedness of the nonlinear Schrödinger equation (NLS) with the quadratic nonlinearity ${\bar{u}}^{2}$ , posed on one-dimensional and two-dimensional tori. While the relevant bilinear estimate with respect to the $X^{s, b}$ -space is known to fail when the regularity s is below some threshold value, we establish local well-posedness for such low regularity by introducing modifications on the $X^{s, b}$ -space.

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来源期刊

Journal of Dynamics and Differential Equations 数学-数学

CiteScore

3.30

自引率

7.70%

发文量

116

审稿时长

>12 weeks

期刊介绍： Journal of Dynamics and Differential Equations serves as an international forum for the publication of high-quality, peer-reviewed original papers in the field of mathematics, biology, engineering, physics, and other areas of science. The dynamical issues treated in the journal cover all the classical topics, including attractors, bifurcation theory, connection theory, dichotomies, stability theory and transversality, as well as topics in new and emerging areas of the field.