非径向聚焦非齐次非线性Schrödinger-Choquard方程的散射

IF 0.9 3区数学 Q2 MATHEMATICS

Acta Mathematica Sinica-English Series Pub Date : 2025-07-15 DOI:10.1007/s10114-025-4015-7

Chengbin Xu

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引用次数: 0

摘要

本文研究了Schrödinger-Choquard方程$${\rm{i}}{\partial _t}u + \Delta u = - ( {{I_\alpha } * {{\vert \cdot \vert}^b}{{\vert u \vert}^p}} ){\vert \cdot \vert^b}{\vert u \vert^{p - 2}}u.$$全局解的长期行为。受Murphy给出非径向INLS散射的简单证明的启发，我们发现非齐次项∣x∣b可以代替径向Sobolev嵌入定理，这使得我们可以证明临界间情况下能量空间中基态以下的散射理论，而不需要径向假设。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Scattering for the Non-Radial Focusing Inhomogeneous Nonlinear Schrödinger–Choquard Equation

In this paper, we study the long-time behavior of global solutions to the Schrödinger–Choquard equation

$${\rm{i}}{\partial _t}u + \Delta u = - ( {{I_\alpha } * {{\vert \cdot \vert}^b}{{\vert u \vert}^p}} ){\vert \cdot \vert^b}{\vert u \vert^{p - 2}}u.$$

Inspired by Murphy who gave a simple proof of scattering for the non-radial INLS, we find that the inhomogeneous term ∣x∣^b can replace the radial Sobolev embedding theorem, which allows us to prove scattering theory below the ground state for the intercritical case in energy space without radial assumption.

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来源期刊

Acta Mathematica Sinica-English Series 数学-数学

CiteScore

1.00

自引率

0.00%

发文量

138

审稿时长

14.5 months

期刊介绍： Acta Mathematica Sinica, established by the Chinese Mathematical Society in 1936, is the first and the best mathematical journal in China. In 1985, Acta Mathematica Sinica is divided into English Series and Chinese Series. The English Series is a monthly journal, publishing significant research papers from all branches of pure and applied mathematics. It provides authoritative reviews of current developments in mathematical research. Contributions are invited from researchers from all over the world.