AI 中文总结
研究具有热效应的非等熵可压缩流体-粒子相互作用模型。通过建立先验估计并取极限，证明该模型存在全局经典解且有最优衰减率，改进前人结果，证实爱因斯坦预测，揭示粒子对模型产生新耗散效应，开发新思想技术克服相关障碍。
AI 中文摘要
爱因斯坦指出流体温度显著影响悬浮粒子运动。为更精确描述此物理过程中温度的影响，Boudin等人引入了一个新的流体-粒子相互作用模型。Mu和Wang通过添加粘性和热传导项建立了平衡态附近经典解的全局存在性。本文通过建立关于粘性和热传导系数的一致先验估计，并取粘性和热传导联合零极限，表明Boudin等人引入的模型仍存在全局经典解并具有最优衰减率，改进了Mu和Wang的结果并证实了爱因斯坦的预测。我们的工作表明粒子的存在确实通过粒子与流体的宏观速度和温度差异对非等熵可压缩流体-粒子模型产生了新的耗散效应，这与纯非等熵可压缩欧拉方程的情况有显著不同。为实现这些目标，我们开发了新的思想和技术来克服因缺乏粘性和热传导以及流体与粒子间非线性相互作用所带来的重大障碍。
英文摘要
In Einstein's seminal work [Ann. Physik, 17 (1905), 549-560], he pointed out that the temperature of a fluid influences the motion of suspended particles dramatically. To describe the effect of the temperature in this physical process more precisely, Boudin et al. [ESAIM Proc., 28 (2009), 195-210] introduced a new fluid-particle interaction model containing of the non-isentropic compressible Euler equations for the fluid and a nonlinear Vlasov-Fokker-Planck type equation for the particles. By adding some viscous and heat conductive terms to the fluid part of this model, Mu and Wang [Calc. Var. Partial Differential Equations, 59 (2020), Paper no. 110] established the global existence of classical solutions near an equilibrium state. In this paper, through establishing the uniform a priori estimates with respect to the viscosity and heat conductivity coefficients and taking the combined zero viscosity and heat conductivity limits, we show that the model introduced by Boudin et al. still admits a global classical solution and enjoys optimal decay rates thereby improving Mu and Wang's results and confirming Einstein's predications. Our work indicates that the presence of particles indeed emanates new dissipation effects on the non-isentropic compressible fluid-particle model via the differences between the macroscopic velocity of the particles and the fluid velocity, and the macroscopic temperature of the particles and the fluid temperature, which is significantly different from the case of pure non-isentropic compressible Euler equations. To achieve these goals, we have developed new ideas and techniques to surmount substantial obstacles caused by the absence of viscosity and heat conductivity, and the nonlinear interactions between the fluid and particles.
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