Geodesic
On the existence of a global solution of the modified Navier--Stokes equations
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 77 (2016) no. 2, pp. 219-249

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We prove global existence theorems for initial-boundary value problems for the modified Navier–Stokes equations used when modeling ocean dynamic processes. First, the case of distinct vertical and horizontal viscosities for the Navier–Stokes equations is considered. Then a result due to Ladyzhenskaya for the modified Navier–Stokes equations is improved, whereby the elliptic operator is strengthened with respect to the horizontal variables alone and only for the horizontal momentum equations. Finally, the global existence and uniqueness of a solution is proved for the primitive equations describing the large-scale ocean dynamics. 
@article{MMO_2016_77_2_a2,
     author = {G. M. Kobel'kov},
     title = {On the existence of a global solution of the modified {Navier--Stokes} equations},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {219--249},
     publisher = {mathdoc},
     volume = {77},
     number = {2},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2016_77_2_a2/}
}
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G. M. Kobel'kov. On the existence of a global solution of the modified Navier--Stokes equations. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 77 (2016) no. 2, pp. 219-249. http://geodesic.mathdoc.fr/item/MMO_2016_77_2_a2/