Global convergence rates from relaxed Euler equations to Navier–Stokes equations with Oldroyd-type constitutive laws

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED

Nonlinearity Pub Date : 2024-08-14 DOI:10.1088/1361-6544/ad68b7

Yue-Jun Peng, Liang Zhao

引用次数: 0

Abstract

In a previous work (Peng and Zhao 2022 J. Math. Fluid Mech. 24 29), it is proved that the 1D full compressible Navier–Stokes equations for a Newtonian fluid can be approximated globally-in-time by a relaxed Euler-type system with Oldroyd’s derivatives and a revised Cattaneo’s constitutive law. These two relaxations turn the whole system into a first-order quasilinear hyperbolic one with partial dissipation. In this paper, we establish the global convergence rates between the smooth solutions to the relaxed Euler-type system and the Navier–Stokes equations over periodic domains. For this purpose, we use stream function techniques together with energy estimates for error systems. These techniques may be applicable to more complicated systems.

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从松弛欧拉方程到含奥尔德罗伊德型构成律的纳维-斯托克斯方程的全局收敛率

在之前的一项工作（Peng 和 Zhao 2022 J. Math. Fluid Mech.24 29）中，证明了牛顿流体的一维完全可压缩纳维-斯托克斯方程可以通过一个具有 Oldroyd 导数和修正的 Cattaneo 构成律的松弛欧拉型系统进行全局实时近似。这两项松弛将整个系统转化为具有部分耗散的一阶准线性双曲系统。在本文中，我们确定了松弛欧拉型系统的光滑解与周期域上的纳维-斯托克斯方程之间的全局收敛率。为此，我们使用了流函数技术和误差系统的能量估计。这些技术可能适用于更复杂的系统。

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

Nonlinearity 物理-物理：数学物理

CiteScore

3.00

自引率

5.90%

发文量

170

审稿时长

12 months

期刊介绍： Aimed primarily at mathematicians and physicists interested in research on nonlinear phenomena, the journal''s coverage ranges from proofs of important theorems to papers presenting ideas, conjectures and numerical or physical experiments of significant physical and mathematical interest. Subject coverage: The journal publishes papers on nonlinear mathematics, mathematical physics, experimental physics, theoretical physics and other areas in the sciences where nonlinear phenomena are of fundamental importance. A more detailed indication is given by the subject interests of the Editorial Board members, which are listed in every issue of the journal. Due to the broad scope of Nonlinearity, and in order to make all papers published in the journal accessible to its wide readership, authors are required to provide sufficient introductory material in their paper. This material should contain enough detail and background information to place their research into context and to make it understandable to scientists working on nonlinear phenomena. Nonlinearity is a journal of the Institute of Physics and the London Mathematical Society.