AI 中文总结
研究紧致连续内部态上与可逆马尔可夫算子耦合的不可压缩 FENE 哑铃模型，零质心扩散时通过无迹矩阵纤维演化证明投影 - 提升等价性等，正质心扩散时构造弱解，明确结果非有限物种约化。
AI 中文摘要
我们考虑在紧致连续内部态上与可逆马尔可夫算子耦合的不可压缩 FENE 哑铃模型。在零质心扩散时，证明态平均是精确的因子映射，拉格朗日态提升是其自然能量解类上的唯一逆。通过无迹矩阵纤维演化驱动提升，允许非线性局部活动。对于有相对熵准备的初始纤维且无粘性耗散缺陷的态分辨正则化，完整密度在标量极限后无需重构就强烈收敛。论证结合正则拉格朗日流稳定性与相对熵估计。正质心扩散时构造了全局大数据弱解并识别出相同非线性项。明确的无限秩核证明这些结果不是有限物种约化。
英文摘要
We consider incompressible FENE dumbbells coupled to a reversible Markov operator on a compact continuum of internal states. At zero centre-of-mass diffusion we prove that state averaging is an exact factor map and that a Lagrangian state lift is its unique inverse on the natural energy-solution classes. Thus existence, multiplicity, and uniqueness of the state-resolved system are precisely those of its scalar FENE projection; the internal-state dynamics creates no additional large-data nonuniqueness. The lift is driven by a trace-free matrix fibre evolution and permits nonlinear local activities, including rates with linear dependence on the singular Kramers stress.We also prove a sequential form of this structure. For state-resolved regularizations with relative-entropy-prepared initial fibres and no viscous dissipation defect, the complete densities converge strongly without reconstructing them after the scalar limit. Consequently the full drag,state-dependent activity, singular stress, and non-atomic Jeffreys production all pass to the limit. The argument combines stability of regular Lagrangian flows with a relative-entropy estimate for simultaneously varying matrix drifts and jump rates. A stationary oscillation shows that the preparation cannot follow from the natural entropy bounds alone. With positive centre-of-mass diffusion we independently construct global large-data weak solutions and identify the same nonlinear terms. An explicit infinite-rank kernel proves that these results are not finite-species reductions.
