Geodesic
Time periodic solutions of the smooth convergent and dissipative $\varepsilon$-approximations for the modified Navier--Stokes equations.
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 116-130

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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. 
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     author = {A. P. Oskolkov},
     title = {Time periodic solutions of the smooth convergent and dissipative $\varepsilon$-approximations for the modified {Navier--Stokes} equations.},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {116--130},
     publisher = {mathdoc},
     volume = {213},
     year = {1994},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a6/}
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A. P. Oskolkov. Time periodic solutions of the smooth convergent and dissipative $\varepsilon$-approximations for the modified Navier--Stokes equations.. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 25, Tome 213 (1994), pp. 116-130. http://geodesic.mathdoc.fr/item/ZNSL_1994_213_a6/