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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