Nonlocal problems of the theory of the equations of motion for Kelvin–Voight fluids

The following nonlocal problems for the threedimensional equations of motion of Kelvin–Veight fluids (14) are studied: global classical solvability on the semiaxis $\mathbb{R}^+$ initial boundary-value problem (14), (15) in the class $W^1_\infty(\mathbb{R}^+;W_2^2(\Omega)\cap H(\Omega))$; the principle of linearized stability and stability of steady solutions and time periodic solutions; global existence theorem of time periodic solutions of equations (14) in the class $W^1_\infty(\mathbb{R}^+;W_2^2(\Omega)\cap H(\Omega))$ with time periodic external force $f(x,t)\in L_\infty(\mathbb{R}^+;L_2(\Omega))$.