On the dynamical system associated with two dimensional equations of the motion of Bingham fluid

In this paper we study solvability, uniqueness and regularity of the solution of the evolutional variational inequality arising in the theory of the motion of two dimensional Bingham fluid. Under some conditions it is proved that family of resolving operators is the semigroup which has the minimal global $B$-attractor $\mathfrak{M}_\lambda$. It is shown that for some values of the parameter $\lambda$ the structure of the attractor $\mathfrak{M}_\lambda$ is trivial. Some estimate of the dimension of the attractor $\mathfrak{M}_\lambda$ is given.