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

Abstract

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.