Time periodic solutions of the smooth convergent and dissipative $\varepsilon$-approximations for the modified Navier–Stokes equations.

In this paper we prove global existence of time-periodic classical solutions $v^\varepsilon$ of dissipative $\varepsilon$-approximations (4)–(6) for three-dimensional modified Navier–Stokes equations (1)–(3) satysfying a first boundary condition, and also we study the convergence for $\varepsilon\to0$ of solutions $\{v^\varepsilon\}$ to time-periodic classical solutions $v$ of equations (1)–(3) respectively. Bibliography: 21 titles.