Optimal temporal decay rates of solutions for combustion of compressible fluids

IF 1.4 3区 数学 Q1 MATHEMATICS
Shengbin Fu, Wenting Huang, Weiwei Wang
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引用次数: 0

Abstract

This paper investigates the temporal decay rates of solutions to the Cauchy problem of a model, which describes the combustion of the compressible fluid. Suppose that the initial data is a small perturbation near the equilibrium state \((\rho _\infty , 0,\theta _\infty ,\zeta )\), where \(\rho _\infty >0\), \(\theta _\infty <\theta _I\) (the ignition temperature), and \(0< \zeta \leqslant 1\), we first establish the global-in-time existence of strong solutions via a standard continuity argument. With the additional \(L^1\)-integrability of the initial perturbation, we then employ the Fourier theory and the cancellation mechanism of low-medium frequent part to derive the optimal temporal decay rates of all-order derivatives of strong solutions. Our work is a natural continuation of previous result in the case of \(\theta _\infty >\theta _I\) discussed in Wang and Wen (Sci China Math 65:1199–1228 (2022).

可压缩流体燃烧解决方案的最佳时间衰减率
本文研究了描述可压缩流体燃烧的模型的考奇问题解的时间衰减率。假设初始数据是平衡态附近的小扰动 \((\rho _\infty , 0,\theta _\infty ,\zeta )\), 其中 \(\rho _\infty >0\), \(\theta _\infty <;\点火温度)和 (0< \zeta \leqslant 1),我们首先通过标准连续性论证建立强解的全局-时间存在性。有了初始扰动的额外的 \(L^1\)-integrability 性,我们就可以利用傅里叶理论和中低频部分的抵消机制来推导强解的全阶导数的最优时间衰减率。我们的工作是王文(Sci China Math 65:1199-1228 (2022))在 \(\theta _\infty >\theta _I\)情况下所讨论结果的自然延续。
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
Analysis and Mathematical Physics
Analysis and Mathematical Physics MATHEMATICS, APPLIED-MATHEMATICS
CiteScore
2.70
自引率
0.00%
发文量
122
期刊介绍: Analysis and Mathematical Physics (AMP) publishes current research results as well as selected high-quality survey articles in real, complex, harmonic; and geometric analysis originating and or having applications in mathematical physics. The journal promotes dialog among specialists in these areas.
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