Global Existence of Classical Solutions for a Reactive Polymeric Fluid near Equilibrium

TL;DR

This paper proves the global existence of classical solutions for a reactive polymeric fluid model near equilibrium, addressing complex chemo-mechanical coupling effects using advanced mathematical inequalities.

Contribution

It introduces a new micro-macro model for reactive polymers and establishes global solutions near equilibrium, highlighting the treatment of chemo-mechanical coupling effects.

Findings

Proved global existence of classical solutions near equilibrium.

Developed a weighted Poincaré inequality to handle non-conservative densities.

Addressed chemo-mechanical coupling in reactive polymeric fluids.

Abstract

In this paper, we study a new micro-macro model for a reactive polymeric fluid, which is derived recently in [Y. Wang, T.-F. Zhang, and C. Liu, \emph{J. Non-Newton. Fluid Mech.} 293 (2021), 104559, 13 pp], by using the energetic variational approach. The model couples the breaking/reforming reaction scheme of the microscopic polymers with other mechanical effects in usual viscoelastic complex fluids. We establish the global existence of classical solutions near the global equilibrium, in which the treatment on the chemo-mechanical coupling effect is the most crucial part. In particular, a weighted Poincar\'e inequality with a mean value is employed to overcome the difficulty that arises from the non-conservative number density distribution of each species.