无穷大质量低正则性空间中的非线性Schrödinger方程

IF 1.8 4区数学 Q1 MATHEMATICS

Differential and Integral Equations Pub Date : 2020-11-06 DOI:10.57262/die035-0708-371

Vanessa Barros, Simão Correia, Filipe Oliveira

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引用次数: 1

摘要

我们研究了初始数据为$\mathcal｛Z｝^s_p（\mathbb｛R｝^d）=\dot｛H｝^s（\mathbb{R｝^ d）\cop L^ p（\math bb｛R｝^）$的非线性Schr“odinger方程，其中$0＜s＜min\｛d/2,1｝$和$2＜p＜2d/（d-2s）$。在证明线性Schr”odinger群在该空间中是明确的之后，我们证明了整个参数范围内的局部适定性性。解的精确性质取决于非线性的幂和可积性$p$之间的关系。最后，我们使用傅立叶截断方法的一个变体，给出了具有无限质量和能量的初始数据的三维散焦三次方程的全局存在性结果。

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On the nonlinear Schrödinger equation in spaces of infinite mass and low regularity

We study the nonlinear Schr\"odinger equation with initial data in $\mathcal{Z}^s_p(\mathbb{R}^d)=\dot{H}^s(\mathbb{R}^d)\cap L^p(\mathbb{R}^d)$, where $0

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来源期刊

Differential and Integral Equations MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

2.40

自引率

0.00%

发文量

审稿时长

6-12 weeks

期刊介绍： Differential and Integral Equations will publish carefully selected research papers on mathematical aspects of differential and integral equations and on applications of the mathematical theory to issues arising in the sciences and in engineering. Papers submitted to this journal should be correct, new, and of interest to a substantial number of mathematicians working in these areas.

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