Well-Posedness and Dynamics of the McKean-Vlasov Stochastic 2D Navier-Stokes Equations Driven by Nonlinear Noise

In this paper, we are concerned with the dynamical behavior of solutions of the non-autonomous McKean-Vlasov stochastic 2D Navier-Stokes equation driven by nonlinear multiplicative noise. Under appropriate assumptions on the nonlinear external force and the noise operator, we first establish the global well-posedness of strong solutions. Next, we prove that the non-autonomous dynamical system generated by the solution operators admits a unique pullback measure attractor in the space of probability measures. Finally, we demonstrate the upper semicontinuity of the pullback measure attractors as the intensity of noise approaches zero.