Temporal asymptotics for the p'th power Newtonian fluid in one space dimension

摘要

The balance laws of mass, momentum and energy are considered for a p'th power Newtonian fluid undergoing one dimensional longitudinal motions. For initial-boundary value problems involving fixed endpoints held at a prescribed temperature or insulated, we prove exponential convergence of solutions to equilibria for generic initial data. The estimates for different boundary conditions are presented in a unified manner by utilising the thermodynamic concept of availability.