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

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