Geodesic
Special global regular solutions to the Navier--Stokes equations
Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 39, Tome 362 (2008), pp. 120-152

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We present the existence results of global regular solutions to the Navier–Stokes equations which are close either to two-dimensional or to axially-symmetric solutions. We assume the slip-boundary conditions. Moreover, the considered domains are either cylindrical or axially symmetric. We examine problems with and without inflow-outflow. All proofs can be divided into two steps: 1. long time existence by either the Leray–Schauder fixed point theorem or the method of successive approximations, 2. global existence by prolongation of the local solution with respect to time. Bibl. – 32 titles. 
@article{ZNSL_2008_362_a5,
     author = {W. M. Zaj\k{a}czkowski},
     title = {Special global regular solutions to the {Navier--Stokes} equations},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {120--152},
     publisher = {mathdoc},
     volume = {362},
     year = {2008},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a5/}
}
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W. M. Zajączkowski. Special global regular solutions to the Navier--Stokes equations. Zapiski Nauchnykh Seminarov POMI, Boundary-value problems of mathematical physics and related problems of function theory. Part 39, Tome 362 (2008), pp. 120-152. http://geodesic.mathdoc.fr/item/ZNSL_2008_362_a5/