d中二次梁方程的柯西问题 ≥ 2

IF 1.7 2区数学 Q1 MATHEMATICS

Journal of Functional Analysis Pub Date : 2025-04-29 DOI:10.1016/j.jfa.2025.111041

Zihao Song

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引用次数: 0

摘要

本文的目的是研究具有二次非线性的梁方程的柯西问题。利用Strichartz估计策略、色散估计策略和时空共振方法，建立了2≤d≤8区间小解的全局适定性和散射性。主要困难在于光束半群的弱色散估计和可能的共振。我们将利用空时共振的零结构观测，这使我们能够获得足够的衰减而避免简并。

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The Cauchy problem for the quadratic beam equation in d ≥ 2

The purpose of this paper is to study the Cauchy problem of the beam equation with quadratic nonlinearity. We establish the global well-posedness and scattering of small solutions in

2 \leq d \leq 8

with the strategy of Strichartz estimates, dispersive estimates and the method of space-time resonance. The main difficulties come from the weak dispersive estimates of beam semi-group and possible resonance. We shall utilize the observation of null structure for space-time resonance, which enables us to obtain enough decay but avoiding the degeneracies.

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来源期刊

Journal of Functional Analysis 数学-数学

CiteScore

3.20

自引率

5.90%

发文量

271

审稿时长

7.5 months

期刊介绍： The Journal of Functional Analysis presents original research papers in all scientific disciplines in which modern functional analysis plays a basic role. Articles by scientists in a variety of interdisciplinary areas are published. Research Areas Include: • Significant applications of functional analysis, including those to other areas of mathematics • New developments in functional analysis • Contributions to important problems in and challenges to functional analysis

d中二次梁方程的柯西问题 ≥ 2

摘要

d中二次梁方程的柯西问题 ≥ 2