The Ladyzhenskaya fluid model is proposed to describe more complex physical phenomena of non-Newtonian fluid flow in 1960s. This paper is concerned with the determination of the nonautonomous three-dimensional Ladyzhenskaya model with shear-dependent viscosity equipped with periodic boundary conditions. Under suitable assumptions on the monotonicity of stress tensor, the boundedness of determining modes is estimated for our considered model via the generalized Grashof number by means of energy estimates and the properties of some operators.
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