Existence and asymptotic stability of time-dependent poiseuille flows of isothermal bipolar fluids

摘要

The existence of both weak and classical solutions, for an initial-boundary value problem associated with the time-dependent Poiseuille flow of a non-linear isothermal bipolar fluid in a channel, is established along with companion results on uniqueness and asymptotic stability. The existence proof is obtained by combining an iteration scheme for the quasilinear parabolic equation governing the velocity of the dipolar fluid with a priori estimates for a class of associated linear prarbolic initial-boundary value problems.