This article is devoted to a coupled microscopic/macroscopic model describing the evolution of particles dispersed in a fluid. The system consists in a Vlasov‐Fokker‐Planck equation to describe the microscopic motion of the particles coupled to the equations for a compressible non‐Newtonian fluid. An initial‐boundary value problem is studied in a bounded domain with the divergence of the velocity field keeping bounded. The existence of global weak solution is established through an approximation scheme, a fixed point argument, the lower semi‐continuity of monotone operators, energy estimates and the principle of compensated compactness.

中文翻译：

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Vlasov-Fokker-Planck /可压缩非牛顿流体方程组的整体弱解

本文致力于描述微观/宏观耦合模型，该模型描述了分散在流体中的颗粒的演化。该系统包含一个Vlasov-Fokker-Planck方程，用于描述与可压缩非牛顿流体方程耦合的颗粒的微观运动。在有界域中研究了初边值问题，速度场的发散保持有界。全局弱解的存在是通过逼近方案，不动点参数，单调算子的下半连续性，能量估计和补偿紧度原理建立的。