On weak solutions to a class of non-Newtonian incompressible fluids in bounded three-dimensional domains: the case $p\geq2$

Abstract

Existence and regularity properties of solutions for the evolutionary system describing unsteady flows of incompressible fluids with shear dependent viscosity are studied. The problem is considered in a bounded, smooth domain of $\mathbb R ^3$ with Dirichlet boundary conditions. The nonlinear elliptic operator, which is related to the stress tensor, has $p$ structure. The paper deals with the case $p\ge 2$, for which the existence of weak solutions is proved. If $p\ge \frac{9}{4}$ then a weak solution is strong and unique among all weak solutions.

Article information

Source
Adv. Differential Equations, Volume 6, Number 3 (2001), 257-302.

Dates
First available in Project Euclid: 2 January 2013

Málek, J.; Nečas, J.; Růžička, M. On weak solutions to a class of non-Newtonian incompressible fluids in bounded three-dimensional domains: the case $p\geq2$. Adv. Differential Equations 6 (2001), no. 3, 257--302. https://projecteuclid.org/euclid.ade/1357141212