{"title":"On the Equations of Compressible Fluid Dynamics With Cattaneo-Type Extensions for the Heat Flux: Symmetrizability and Relaxation Structure","authors":"Felipe Angeles","doi":"10.1111/sapm.12790","DOIUrl":null,"url":null,"abstract":"<div>\n \n <p>The aim of this work is twofold. From a mathematical point of view, we show the existence of a hyperbolic system of equations that is not symmetrizable in the sense of Friedrichs. Such system appears in the theory of compressible fluid dynamics with Cattaneo-type extensions for the heat flux. In contrast, the linearizations of such system around constant equilibrium solutions have Friedrichs symmetrizers. Then, from a physical perspective, we aim to understand the relaxation term appearing in this system. By noticing the violation of the Kawashima–Shizuta condition, locally and smoothly, with respect to the Fourier frequencies, we construct persistent waves, that is, solutions preserving the <span></span><math>\n <semantics>\n <msup>\n <mi>L</mi>\n <mn>2</mn>\n </msup>\n <annotation>$L^{2}$</annotation>\n </semantics></math> norm for all times that are not dissipated by the relaxation terms.</p></div>","PeriodicalId":51174,"journal":{"name":"Studies in Applied Mathematics","volume":"154 1","pages":""},"PeriodicalIF":2.6000,"publicationDate":"2024-11-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Studies in Applied Mathematics","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1111/sapm.12790","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
The aim of this work is twofold. From a mathematical point of view, we show the existence of a hyperbolic system of equations that is not symmetrizable in the sense of Friedrichs. Such system appears in the theory of compressible fluid dynamics with Cattaneo-type extensions for the heat flux. In contrast, the linearizations of such system around constant equilibrium solutions have Friedrichs symmetrizers. Then, from a physical perspective, we aim to understand the relaxation term appearing in this system. By noticing the violation of the Kawashima–Shizuta condition, locally and smoothly, with respect to the Fourier frequencies, we construct persistent waves, that is, solutions preserving the norm for all times that are not dissipated by the relaxation terms.
这项工作有两个目的。从数学角度看，我们证明了弗里德里希斯意义上不可对称的双曲方程组的存在。这种系统出现在热通量的卡塔尼奥型扩展的可压缩流体力学理论中。相反，围绕恒定平衡解的线性化系统具有弗里德里希对称性。然后，从物理角度出发，我们旨在理解该系统中出现的松弛项。通过注意与傅立叶频率有关的局部和平滑的川岛-志津田条件的违反，我们构建了持久波，即在所有时间内都保持 L 2 $L^{2}$ 准则的解，而这些解并没有被松弛项耗散。
期刊介绍：
Studies in Applied Mathematics explores the interplay between mathematics and the applied disciplines. It publishes papers that advance the understanding of physical processes, or develop new mathematical techniques applicable to physical and real-world problems. Its main themes include (but are not limited to) nonlinear phenomena, mathematical modeling, integrable systems, asymptotic analysis, inverse problems, numerical analysis, dynamical systems, scientific computing and applications to areas such as fluid mechanics, mathematical biology, and optics.
求助内容：
应助结果提醒方式：
京公网安备 11010802042870号
