2025/07/04 by Gao, Jincheng, Wu, Jiahong, Yao, Zheng-an +1
#35Q30 #76A10 #Analysis of PDEs (math.AP) #FOS: Mathematics #Primary: 35Q35 #Secondary: 35B40
paper · doi:10.48550/arxiv.2507.03533
In this work, we study the global-in-time incompressible limit of the compressible FENE dumbbell model on the three-dimensional torus T3, where the incompressible limit is driven by large volume viscosity. To establish this limit, we develop time-weighted a priori estimates that yield decay rates for strong solutions. A key challenge arises from the fact that increasing the volume viscosity suppresses the decay of high-frequency components, thereby weakening the dissipation of the density and complicating the derivation of uniform-in-time decay estimates. To overcome this difficulty, we introduce a novel momentum-based estimate and show that the incompressible component of the momentum decays faster in time than the velocity itself. Exploiting this enhanced decay, we successfully close the a priori estimates and establish a time-decreasing convergence rate toward the incompressible limit.