Globally Analytical Solutions of the Compressible Oldroyd-B Model Without Retardation

IF 2.2 2区数学 Q1 MATHEMATICS, APPLIED

SIAM Journal on Mathematical Analysis Pub Date : 2024-07-05 DOI:10.1137/23m1588974

Xinghong Pan

引用次数: 0

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.

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无缓速可压缩奥尔德罗伊德-B 模型的全局分析解决方案

SIAM 数学分析期刊》，第 56 卷第 4 期，第 4854-4869 页，2024 年 8 月。摘要本文证明了[math][math]中可压缩 Oldroyd-B 模型在非真空平衡附近无延迟的全局存在解析解。零迟滞导致速度方程中的零耗散，这是阻碍我们获得长时间良好求解的主要困难。通过专门分析，我们发现该模型的线性化方程具有阻尼效应，这确保了小数据解的全局时间存在性。然而，非线性二次项比线性部分多了一阶导数，目前还没有发现克服导数损失问题的良好结构。因此，我们只能在分析能量空间而不是具有有限阶导数的 Sobolev 空间中建立结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.