一维非平衡流的时间渐近行为

IF 2.7 3区数学 Q1 MATHEMATICS, APPLIED

Physica D: Nonlinear Phenomena Pub Date : 2025-03-31 DOI:10.1016/j.physd.2025.134647

Yanni Zeng

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引用次数: 0

摘要

我们研究了多原子气体在平动和振动两种非平衡状态下的长时间行为。作者先前建立了柯西问题解的全局存在性，并获得了柯西问题趋于平衡态解的最优L2时间衰减率。本文是对解行为研究的延续。利用沿粒子路径的一个热核和沿平衡声学方向的两个Burgers核明确地构造了渐近解。从空间和时间的角度研究了精确解的渐近解的收敛性，给出了波传播的全貌。该研究为未来研究激波周围溶液的行为奠定了基础，激波是混合问题中引起richmyer - meshkov不稳定性的机制。

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Time asymptotic behavior of non-equilibrium flows in one space dimension

We study long time behavior of polyatomic gas flows in both translational and vibrational non-equilibrium. The author previously established global existence of solution and obtained optimal

L^{2}

time-decay rates for the solution towards an equilibrium state for the Cauchy problem. The current paper is a continuation in studying the solution behavior. An asymptotic solution is constructed explicitly using a heat kernel along the particle path and two Burgers kernels along the equilibrium acoustic directions. Convergence of the exact solution to the asymptotic solution is studied in a pointwise sense in both space and time to give a complete picture of wave propagation. The study lays a foundation for a future work on solution behavior around a shock wave, a mechanism that induces Richtmyer–Meshkov instability in mixing problems .

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来源期刊

Physica D: Nonlinear Phenomena 物理-物理：数学物理

CiteScore

7.30

自引率

7.50%

发文量

213

审稿时长

65 days

期刊介绍： Physica D (Nonlinear Phenomena) publishes research and review articles reporting on experimental and theoretical works, techniques and ideas that advance the understanding of nonlinear phenomena. Topics encompass wave motion in physical, chemical and biological systems; physical or biological phenomena governed by nonlinear field equations, including hydrodynamics and turbulence; pattern formation and cooperative phenomena; instability, bifurcations, chaos, and space-time disorder; integrable/Hamiltonian systems; asymptotic analysis and, more generally, mathematical methods for nonlinear systems.