Ufa Mathematical Journal
    Volume 5, Number 4, pp. 58-74

    Modified gradient fastest descent method for solving linearized non-stationary Navier-Stokes equations

    Golichev I.I.


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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.