无界域辐射流体力学模型的全局经典大解

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-04 DOI:10.1137/23m1598581

Jing Wei, Minyi Zhang, Changjiang Zhu

{"title":"无界域辐射流体力学模型的全局经典大解","authors":"Jing Wei, Minyi Zhang, Changjiang Zhu","doi":"10.1137/23m1598581","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4811-4833, August 2024. <br/> Abstract. This paper is concerned with the global existence of large solutions to the initial and initial boundary value problems for the radiation hydrodynamics model with constant viscosity coefficient and temperature-dependent heat conductivity coefficient. In particular, the initial data and [math] could be arbitrarily large. Compared with the classical compressible Navier–Stokes equations, the research on the radiation hydrodynamics model is more complicated due to the presence of the radiation effect. To overcome difficulties caused by the radiation, inspired by [J. Li and Z. L. Liang, Arch. Ration. Mech. Anal., 220 (2016), pp. 1195–1208; J. H. Zhang and H. J. Zhao, SIAM J. Math. Anal., 55 (2023), pp. 6229–6261], we construct a pointwise estimate between the radiative heat flux and the temperature; then we can establish the desired basic energy estimate by considering that the temperature has lower and upper bounds separately. And once that is obtained, the main result is proved by employing the elementary energy methods.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Global Classical Large Solutions for the Radiation Hydrodynamics Model in Unbounded Domains\",\"authors\":\"Jing Wei, Minyi Zhang, Changjiang Zhu\",\"doi\":\"10.1137/23m1598581\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4811-4833, August 2024. <br/> Abstract. This paper is concerned with the global existence of large solutions to the initial and initial boundary value problems for the radiation hydrodynamics model with constant viscosity coefficient and temperature-dependent heat conductivity coefficient. In particular, the initial data and [math] could be arbitrarily large. Compared with the classical compressible Navier–Stokes equations, the research on the radiation hydrodynamics model is more complicated due to the presence of the radiation effect. To overcome difficulties caused by the radiation, inspired by [J. Li and Z. L. Liang, Arch. Ration. Mech. Anal., 220 (2016), pp. 1195–1208; J. H. Zhang and H. J. Zhao, SIAM J. Math. Anal., 55 (2023), pp. 6229–6261], we construct a pointwise estimate between the radiative heat flux and the temperature; then we can establish the desired basic energy estimate by considering that the temperature has lower and upper bounds separately. And once that is obtained, the main result is proved by employing the elementary energy methods.\",\"PeriodicalId\":51150,\"journal\":{\"name\":\"SIAM Journal on Mathematical Analysis\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-07-04\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"SIAM Journal on Mathematical Analysis\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1137/23m1598581\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"SIAM Journal on Mathematical Analysis","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1137/23m1598581","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

摘要

SIAM 数学分析期刊》，第 56 卷第 4 期，第 4811-4833 页，2024 年 8 月。摘要本文关注粘性系数恒定、导热系数随温度变化的辐射流体力学模型的初始值和初始边界值问题的全局大解存在性。特别是，初始数据和[math]可以任意大。与经典的可压缩 Navier-Stokes 方程相比，由于辐射效应的存在，辐射流体力学模型的研究更为复杂。为了克服辐射带来的困难，受[J. Li 和 Z. L. Liang]的启发，我们提出了辐射流体力学模型。Li and Z. L. Liang, Arch.Ration.Mech.Anal., 220 (2016), pp.Anal.，55 (2023)，pp. 6229-6261]，我们构建了辐射热通量与温度之间的点估计；然后，我们可以通过考虑温度分别具有下限和上限来建立所需的基本能量估计。得到这些估计值后，我们就可以利用基本能量方法证明主要结果了。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Global Classical Large Solutions for the Radiation Hydrodynamics Model in Unbounded Domains

SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4811-4833, August 2024.
Abstract. This paper is concerned with the global existence of large solutions to the initial and initial boundary value problems for the radiation hydrodynamics model with constant viscosity coefficient and temperature-dependent heat conductivity coefficient. In particular, the initial data and [math] could be arbitrarily large. Compared with the classical compressible Navier–Stokes equations, the research on the radiation hydrodynamics model is more complicated due to the presence of the radiation effect. To overcome difficulties caused by the radiation, inspired by [J. Li and Z. L. Liang, Arch. Ration. Mech. Anal., 220 (2016), pp. 1195–1208; J. H. Zhang and H. J. Zhao, SIAM J. Math. Anal., 55 (2023), pp. 6229–6261], we construct a pointwise estimate between the radiative heat flux and the temperature; then we can establish the desired basic energy estimate by considering that the temperature has lower and upper bounds separately. And once that is obtained, the main result is proved by employing the elementary energy methods.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

SIAM Journal on Mathematical Analysis 数学-应用数学

CiteScore

3.30

自引率

5.00%

发文量

175

审稿时长

12 months

期刊介绍： SIAM Journal on Mathematical Analysis (SIMA) features research articles of the highest quality employing innovative analytical techniques to treat problems in the natural sciences. Every paper has content that is primarily analytical and that employs mathematical methods in such areas as partial differential equations, the calculus of variations, functional analysis, approximation theory, harmonic or wavelet analysis, or dynamical systems. Additionally, every paper relates to a model for natural phenomena in such areas as fluid mechanics, materials science, quantum mechanics, biology, mathematical physics, or to the computational analysis of such phenomena. Submission of a manuscript to a SIAM journal is representation by the author that the manuscript has not been published or submitted simultaneously for publication elsewhere. Typical papers for SIMA do not exceed 35 journal pages. Substantial deviations from this page limit require that the referees, editor, and editor-in-chief be convinced that the increased length is both required by the subject matter and justified by the quality of the paper.