{"title":"The Optimal \\({{\\varvec{L}}^2}\\) Decay Rate of the Velocity for the General FENE Dumbbell Model","authors":"Zhaonan Luo, Wei Luo, Zhaoyang Yin","doi":"10.1007/s00021-024-00880-5","DOIUrl":null,"url":null,"abstract":"<div><p>In this paper we mainly study large time behavior for the strong solutions of the finite extensible nonlinear elastic (FENE) dumbbell model. The sharp <span>\\(L^2\\)</span> decay rate was obtained on the co-rotational case. We prove that the optimal <span>\\(L^2\\)</span> decay rate of the velocity of the general FENE dumbbell model is <span>\\((1+t)^{-\\frac{d}{4}}\\)</span> with <span>\\(d\\ge 2\\)</span>. Our obtained result is sharp and improves considerably the previous result in Luo and Yin (Arch Ration Mech Anal 224(1):209–231, 2017).</p></div>","PeriodicalId":649,"journal":{"name":"Journal of Mathematical Fluid Mechanics","volume":"26 3","pages":""},"PeriodicalIF":1.2000,"publicationDate":"2024-05-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Mathematical Fluid Mechanics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s00021-024-00880-5","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we mainly study large time behavior for the strong solutions of the finite extensible nonlinear elastic (FENE) dumbbell model. The sharp \(L^2\) decay rate was obtained on the co-rotational case. We prove that the optimal \(L^2\) decay rate of the velocity of the general FENE dumbbell model is \((1+t)^{-\frac{d}{4}}\) with \(d\ge 2\). Our obtained result is sharp and improves considerably the previous result in Luo and Yin (Arch Ration Mech Anal 224(1):209–231, 2017).
期刊介绍：
The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.
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