Some nonlocal problems for the modified Navier–Stokes equations

The following nonlocal problems for three-dimensional modified Navier–Stokes equations (3) and (4) are studied: global classical solvability on the semiaxis $t\in\mathbb{R}^+$ initial boundary-value problems (3), (5) and (4), (5); global existence theorems of time periodic solutions of equations (3) and equations (4) with time periodic external force $f$.