Symmetric approximations of the Navier–Stokes equations

A new method for the symmetric approximation of the non-stationary Navier–Stokes equations by a Cauchy–Kovalevskaya-type system is proposed. Properties of the modified problem are studied. In particular, the convergence as $\varepsilon\to0$ of the solutions of the modified problem to the solutions of the original problem on an infinite interval is established.