We consider a dilute suspension of dumbbells joined by a finitely extendible nonlinear elastic connector evolving under the classical Warner potential , . The solvent under consideration is modelled by the compressible Navier–Stokes system defined on the torus with d = 2, 3 coupled with the Fokker–Planck equation (Kolmogorov forward equation) for the probability density function of the dumbbell configuration. We prove the existence of a unique local-in-time solution to the coupled system where this solution is smooth in the spacetime variables and interpreted weakly in the elongation variable. Our result holds true independently of whether or not the centre-of-mass diffusion term is incorporated in the Fokker–Planck equation.

我们考虑在经典 Warner 势下演化的有限可扩展非线性弹性连接器连接的哑铃的稀释悬挂，。所考虑的溶剂由定义在圆环上的可压缩 Navier-Stokes 系统建模，d = 2, 3 加上 Fokker-Planck 方程（Kolmogorov 正向方程），用于哑铃配置的概率密度函数。我们证明了耦合系统的唯一局部时间解的存在，其中该解在时空变量中是平滑的，而在伸长变量中的解释很弱。无论质心扩散项是否包含在 Fokker-Planck 方程中，我们的结果都是正确的。