{"title":"The global existence of strong solutions for a non-isothermal ideal gas system","authors":"","doi":"10.1007/s10473-024-0306-9","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach. We first show the global well-posedness in the Sobolev space <strong><em>H</em></strong><sup>2</sup> (ℝ<sup>3</sup>) for solutions near equilibrium through iterated energy-type bounds and a continuity argument. We then prove the global well-posedness in the critical Besov space <span> <span>\\(\\dot{\\boldsymbol{B}}_{\\boldsymbol{2,1}}^{\\boldsymbol{3/2}}\\)</span> </span> by showing that the linearized operator is a contraction mapping under the right circumstances.</p>","PeriodicalId":50998,"journal":{"name":"Acta Mathematica Scientia","volume":null,"pages":null},"PeriodicalIF":1.2000,"publicationDate":"2024-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Acta Mathematica Scientia","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s10473-024-0306-9","RegionNum":4,"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
We investigate the global existence of strong solutions to a non-isothermal ideal gas model derived from an energy variational approach. We first show the global well-posedness in the Sobolev space H2 (ℝ3) for solutions near equilibrium through iterated energy-type bounds and a continuity argument. We then prove the global well-posedness in the critical Besov space \(\dot{\boldsymbol{B}}_{\boldsymbol{2,1}}^{\boldsymbol{3/2}}\) by showing that the linearized operator is a contraction mapping under the right circumstances.
期刊介绍：
Acta Mathematica Scientia was founded by Prof. Li Guoping (Lee Kwok Ping) in April 1981.
The aim of Acta Mathematica Scientia is to present to the specialized readers important new achievements in the areas of mathematical sciences. The journal considers for publication of original research papers in all areas related to the frontier branches of mathematics with other science and technology.
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