On modifications of the Navier-Stokes equations

摘要

A modification of the Navier-Stokes equations being in some sense generalization of the Ladyzhenskaya modification [2] is considered. Namely, we modify the elliptic operator in the first two motion equations in the same way as Ladyzhenskaya, but in two variables (not three), while the third motion equation is not changed. For the mixed boundary value problem in a bounded domain, existence and uniqueness of a solution 'in the large' is proved. The case of viscosity coefficient different in vertical and horizontal directions is also considered.