**
MATHEMATICA BOHEMICA, Vol. 126, No. 2, pp. 421-428 (2001)
**

# On an evolutionary nonlinear fluid model

in the limiting case

## Stephan Luckhaus, Josef Malek

* Stephan Luckhaus*, Fakultät für Mathematik und Informatik, Universit\" at Leipzig, Augustsplatz 10/11, 04109 Leipzig, Germany

* Josef Malek*, Mathematical Institute, Charles University, Sokolovska 83, 186 75 Praha 8, Czech Republic

**Abstract:**
We consider the two-dimesional spatially periodic problem for an evolutionary system describing unsteady motions of the fluid with shear-dependent viscosity under general assumptions on the form of nonlinear stress tensors that includes those with $p$-structure. The global-in-time existence of a weak solution is established. Some models where the nonlinear operator corresponds to the case $p=1$ are covered by this analysis.

**Keywords:** shear-dependent viscosity, incompressible fluid, global-in-time existence, weak solution

**Classification (MSC2000):** 35Q35, 76D03

**Full text of the article:**

[Previous Article] [Next Article] [Contents of this Number]

*
© 2005 ELibM and
FIZ Karlsruhe / Zentralblatt MATH
for the EMIS Electronic Edition
*