{"title":"Optimal temporal decay rates of solutions for combustion of compressible fluids","authors":"Shengbin Fu, Wenting Huang, Weiwei Wang","doi":"10.1007/s13324-024-00984-1","DOIUrl":null,"url":null,"abstract":"<div><p>This paper investigates the temporal decay rates of solutions to the Cauchy problem of a model, which describes the combustion of the compressible fluid. Suppose that the initial data is a small perturbation near the equilibrium state <span>\\((\\rho _\\infty , 0,\\theta _\\infty ,\\zeta )\\)</span>, where <span>\\(\\rho _\\infty >0\\)</span>, <span>\\(\\theta _\\infty <\\theta _I\\)</span> (the ignition temperature), and <span>\\(0< \\zeta \\leqslant 1\\)</span>, we first establish the global-in-time existence of strong solutions via a standard continuity argument. With the additional <span>\\(L^1\\)</span>-integrability of the initial perturbation, we then employ the Fourier theory and the cancellation mechanism of low-medium frequent part to derive the optimal temporal decay rates of all-order derivatives of strong solutions. Our work is a natural continuation of previous result in the case of <span>\\(\\theta _\\infty >\\theta _I\\)</span> discussed in Wang and Wen (Sci China Math 65:1199–1228 (2022).</p></div>","PeriodicalId":48860,"journal":{"name":"Analysis and Mathematical Physics","volume":"14 6","pages":""},"PeriodicalIF":1.4000,"publicationDate":"2024-11-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Analysis and Mathematical Physics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s13324-024-00984-1","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper investigates the temporal decay rates of solutions to the Cauchy problem of a model, which describes the combustion of the compressible fluid. Suppose that the initial data is a small perturbation near the equilibrium state \((\rho _\infty , 0,\theta _\infty ,\zeta )\), where \(\rho _\infty >0\), \(\theta _\infty <\theta _I\) (the ignition temperature), and \(0< \zeta \leqslant 1\), we first establish the global-in-time existence of strong solutions via a standard continuity argument. With the additional \(L^1\)-integrability of the initial perturbation, we then employ the Fourier theory and the cancellation mechanism of low-medium frequent part to derive the optimal temporal decay rates of all-order derivatives of strong solutions. Our work is a natural continuation of previous result in the case of \(\theta _\infty >\theta _I\) discussed in Wang and Wen (Sci China Math 65:1199–1228 (2022).
期刊介绍:
Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.