乘积空间上准线性波方程系统的全局好求解性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-07-19 DOI:10.2140/apde.2024.17.2033

Cécile Huneau, Annalaura Stingo

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引用次数: 0

摘要

我们考虑的是乘积空间ℝ1+3× ᵔ1上的准线性波方程系统，我们希望将其视为具有额外紧凑维度的爱因斯坦方程的玩具模型。我们证明了对于较小且规则的初始数据，在无穷远处具有多项式衰减的解的全局存在性。该方法结合了对光锥内双曲线的能量估计和对光锥外的加权能量估计。

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Global well-posedness for a system of quasilinear wave equations on a product space

We consider a system of quasilinear wave equations on the product space $ℝ^{1 + 3} \times 𝕊^{1}$ , which we want to see as a toy model for the Einstein equations with additional compact dimensions. We show global existence of solutions for small and regular initial data with polynomial decay at infinity. The method combines energy estimates on hyperboloids inside the light cone and weighted energy estimates outside the light cone.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.