Investigation of the method of nets for two-dimensional equations of the Navier-Stokes and Euler type with non-negative viscosity, I

Abstract

Equations of the Navier-Stokes and Euler type in stream function — vorticity variables, which are encountered in oceanology, are considered. A formulation of the problem and a difference scheme are presented. The unique solvability of the difference problem is proved, a priori estimates of the difference solution are obtained, and the convergence of a certain iterative process for solving the non-linear difference problem is proved.