The Problem of Single – Determinability Equations of Navier-Stokes

Abstract

Abstract. The Navier-Stokes equations describing a viscous incompressible fluid have for many decades attracted the attention of scientists working on the problem of solvability of partial differential equations and specialists in the field of numerical analysis due to numerous applications. Despite such interest, the question of the existence and uniqueness of the “on the whole” solution of the non-stationary Navier-Stokes equations in the case of three spatial variables still remains open. S. Smagulov made a great contribution to the development of the theory and numerical methods for solving initial-boundary value problems for the Navier- Stokes equations. The situation with the numerical solution of these equations is more complex. The fact is that numerical methods that have proven themselves in solving one class of problems are ineffective in solving another class. From the point of view of justification of numerical methods, there is no possibility of using a number of results. The theory of the equation of mathematical physics, since, as mentioned above, they are open to the Navier-Stokes system. Therefore, the young scientist S. Smagulov of the 1970s of the last century, in order to work successfully in this field of mathematics, combined in himself a specialist in differential equations and also in computational mathematics.