Existence and uniqueness results for non-Newtonian fluids of the Oldroyd type in unbounded domains
Volume 70 / 2005
Banach Center Publications 70 (2005), 209-237
MSC: 35Q30, 76A05, 76D03.
DOI: 10.4064/bc70-0-14
Abstract
In the paper \cite{sa2}, we give the full system of equations modelling the motion of a fluid/viscoelastic solid system, and obtain a differential model similar to the so-called Oldroyd model for a viscoelastic fluid. Moreover, existence results in bounded domains are obtained. In this paper we extend the results in \cite{sa2} to unbounded domains. The unique solvability of the system of equations is established locally in time and globally in time with so-called smallness restrictions. Moreover, existence of a weak solution is treated.
