{"title":"Globally Analytical Solutions of the Compressible Oldroyd-B Model Without Retardation","authors":"Xinghong Pan","doi":"10.1137/23m1588974","DOIUrl":null,"url":null,"abstract":"SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4854-4869, August 2024. <br/> Abstract. In this paper, we prove the global existence of analytical solutions to the compressible Oldroyd-B model without retardation near a nonvacuum equilibrium in [math] [math]. Zero retardation results in zero dissipation in the velocity equation, which is the main difficulty that prevents us from obtaining the long time well-posedness of solutions. Through dedicated analysis, we find that the linearized equations of this model have damping effects, which ensure the global-in-time existence of small data solutions. However, the nonlinear quadratic terms have one more order derivative than the linear part and no good structure is discovered to overcome this derivative loss problem. So we can only build the result in the analytical energy space rather than Sobolev space with finite order derivatives.","PeriodicalId":51150,"journal":{"name":"SIAM Journal on Mathematical Analysis","volume":null,"pages":null},"PeriodicalIF":2.2000,"publicationDate":"2024-07-05","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/10.1137/23m1588974","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
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Abstract
SIAM Journal on Mathematical Analysis, Volume 56, Issue 4, Page 4854-4869, August 2024. Abstract. In this paper, we prove the global existence of analytical solutions to the compressible Oldroyd-B model without retardation near a nonvacuum equilibrium in [math] [math]. Zero retardation results in zero dissipation in the velocity equation, which is the main difficulty that prevents us from obtaining the long time well-posedness of solutions. Through dedicated analysis, we find that the linearized equations of this model have damping effects, which ensure the global-in-time existence of small data solutions. However, the nonlinear quadratic terms have one more order derivative than the linear part and no good structure is discovered to overcome this derivative loss problem. So we can only build the result in the analytical energy space rather than Sobolev space with finite order derivatives.
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.
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