Global existence and asymptotic behavior of the full Euler system with damping and radiative effects in $\mathbb{R}^3$

IF 1.2 4区 数学 Q2 MATHEMATICS, APPLIED Communications in Mathematical Sciences Pub Date : 2024-03-04 DOI:10.4310/cms.2024.v22.n3.a8
Shijin Deng, Wenjun Wang, Feng Xie, Xiongfeng Yang
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Abstract

In this paper, we study the global existence and the large-time behavior of solutions to the Cauchy problem of the full Euler system with damping and radiative effects around some constant equilibrium states. It is well-known that the solutions may blow up in finite time without the additional damping and radiative effects, and the global existence of the solutions obtained in this paper shows that these two effects together prevent the formation of the singularity when the initial perturbation is small. Combining the Green’s function method and energy estimates, we consider the pointwise structures of the solutions to obtain a precise description of the system. The construction of the Green’s function includes three steps: singularity removal, long wave-short wave decomposition and weighted energy estimate. Finally, we achieve the pointwise estimates of the solutions in the small perturbation framework by Duhamel’s principle, the pointwise structure of the Green’s function established for the linearized equations and bounded estimates for higher order derivatives of the solutions together.
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在 $\mathbb{R}^3$ 中具有阻尼和辐射效应的全欧拉系统的全局存在性和渐近行为
本文研究了具有阻尼和辐射效应的全欧拉系统 Cauchy 问题解在某些恒定平衡态附近的全局存在性和大时间行为。众所周知,如果没有额外的阻尼和辐射效应,解可能会在有限时间内炸毁,而本文得到的解的全局存在性表明,当初始扰动较小时,这两种效应共同阻止了奇点的形成。结合格林函数方法和能量估计,我们考虑了解的点式结构,从而获得了系统的精确描述。格林函数的构建包括三个步骤:奇点消除、长波-短波分解和加权能量估计。最后,我们通过杜哈梅尔原理、为线性化方程建立的格林函数点式结构以及解的高阶导数有界估计,在小扰动框架下实现了解的点式估计。
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来源期刊
CiteScore
1.70
自引率
10.00%
发文量
59
审稿时长
6 months
期刊介绍: Covers modern applied mathematics in the fields of modeling, applied and stochastic analyses and numerical computations—on problems that arise in physical, biological, engineering, and financial applications. The journal publishes high-quality, original research articles, reviews, and expository papers.
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