Time-periodic solutions of the dissipative $\varepsilon$-approximations for the modified Navies–Stokes equations

The existence of a time-periodic solutions of the perturbed equations (3), (4), (5) and (6) satisfying a free surface condition (9) is proved. It is shown that for $\varepsilon\to0$ the solutions $\{v^\varepsilon\}$ of these problems tends to the solutions of analogous problems for the modified Navies–Stokes equations (1) and (2). Bibliography: 12 titles.