Iterative linearization of the evolution Navier–Stokes equations

Constructed and validated an iterative process, which reduces the solution of nonlinear time-dependent Navier–Stokes equations to the solution of a sequence of linear problems. Using a priori estimates of solutions allows us to prove the convergence of the method with any initial approximation. It is shown that the proposed method can be used to prove the existence and uniqueness of the solution.