In this paper, we study the three-dimensional non-isentropic compressible fluid–particle flows. The system involves coupling between the Vlasov–Fokker–Planck equation and the non-isentropic compressible Navier–Stokes equations through momentum and energy exchanges. For the initial data near the given equilibrium we prove the global well-posedness of strong solutions and obtain the optimal algebraic rate of convergence in the three-dimensional whole space. For the periodic domain the same global well-posedness result still holds while the convergence rate is exponential. New ideas and techniques are developed to establish the well-posedness and large-time behavior. For the global well-posedness our methods are based on the new macro–micro decomposition which involves less dependence on the spectrum of the linear Fokker–Plank operator and fine energy estimates; while the proofs of the optimal large-time behavior rely on the Fourier analysis of the linearized Cauchy problem and the energy-spectrum method, where we provide some new techniques to deal with the nonlinear terms.

在本文中，我们研究了三维非等熵可压缩流体-颗粒流。该系统包括通过动量和能量交换在Vlasov-Fokker-Planck方程和非等熵可压缩Navier-Stokes方程之间进行耦合。对于给定平衡附近的初始数据，我们证明了强解的全局适定性，并在三维整体空间中获得了最佳的代数收敛速度。对于周期域，收敛速度为指数级时，仍保持相同的全局适定性结果。开发了新的思想和技术来建立良好的姿势和长时间的行为。对于全局的适定性，我们的方法基于新的宏观-微观分解，这种分解涉及对线性Fokker-Plank算符的频谱和精细能量估计的依赖性较小；最佳长时间行为的证明依赖于线性柯西问题的傅立叶分析和能量谱方法，在此我们提供了一些处理非线性项的新技术。