Geodesic
Modified gradient fastest descent method for solving linearized non-stationary Navier-Stokes equations
Ufa mathematical journal, Tome 5 (2013) no. 4, pp. 58-74

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We introduce a regularization of Navier-Stokes equations, whose solution coincides with the solution to the system of Navier-Stokes equations if the latter exists. The regularized nonlinear system is reduced to solving a sequence of linearized systems. To solve the latter system, we employ the gradient method. We construct and justify a modified method of fastest descent, which may be employed under restrictions on the control and an unbounded Lebesgue set.
Keywords: Navier-Stokes equations, gradient method, regularization, apriori estimates. 
@article{UFA_2013_5_4_a5,
     author = {I. I. Golichev},
     title = {Modified gradient fastest descent method for solving linearized non-stationary {Navier-Stokes} equations},
     journal = {Ufa mathematical journal},
     pages = {58--74},
     publisher = {mathdoc},
     volume = {5},
     number = {4},
     year = {2013},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/UFA_2013_5_4_a5/}
}
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I. I. Golichev. Modified gradient fastest descent method for solving linearized non-stationary Navier-Stokes equations. Ufa mathematical journal, Tome 5 (2013) no. 4, pp. 58-74. http://geodesic.mathdoc.fr/item/UFA_2013_5_4_a5/