On Solvability of a Fluid Flow Alpha-Model With Memory

We study weak solvability of an alpha-model in non-Newtonian hydrodynamics. If the parameter alpha equals zero, then the alpha-model coincides with the classical one describing a fluid flow with memory. This model takes into account fluid’s memory along trajectories of movement. Additionally, we show that solutions of the alpha-model tend to solutions to the classical model as the parameter alpha tends to zero.