On the navier-stokes equation with the additional condition $u_1^1 = u^3 = 0$

Abstract

We study the Navier-Stokes equation with the additional condition $u_1^1 = u^3 = 0$. In certain cases, solutions are represented in a closed form. In other cases, the investigated system reduces to simpler systems of partial differential equations. We study the symmetry properties of these systems and construct classes of their particular solutions.