论文标题
存在大型数据全球弱解，用于非均匀稀稀聚合物流体的动力学模型
Existence of Large-Data Global Weak Solutions to Kinetic Models of Nonhomogeneous Dilute Polymeric Fluids
论文作者
论文摘要
我们证明了大型全球全球较弱的解决方案存在于一类耦合的珠子弹簧链模型中，具有有限的可扩展的非线性弹性（Fene）类型的弹簧电位，用于在$ \ Mathbb {r}^d $ \ MathBb {r}^d $或$ d $ d $ d $ d $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3 $ 3.所考虑的模型类别涉及纳维尔 - 史托克斯系统的密度可变，其中粘度系数取决于密度和聚合物数密度，并耦合到fokker-planck方程，并具有密度依赖性阻力系数。该证明是基于将概率密度函数与两阶段galerkin近似和弱的紧凑度和补偿紧凑型技术结合在一起的截断，以将galerkin近似序列和截断水平的限制传递到限制。
We prove the existence of large-data global-in-time weak solutions to a general class of coupled bead-spring chain models with finitely extensible nonlinear elastic (FENE) type spring potentials for nonhomogeneous incompressible dilute polymeric fluids in a bounded domain in $\mathbb{R}^d$, $d=2$ or $3$. The class of models under consideration involves the Navier--Stokes system with variable density, where the viscosity coefficient depends on both the density and the polymer number density, coupled to a Fokker--Planck equation with a density-dependent drag coefficient. The proof is based on combining a truncation of the probability density function with a two-stage Galerkin approximation and weak compactness and compensated compactness techniques to pass to the limits in the sequence of Galerkin approximations and in the truncation level.
