# The Cauchy problem for the Stokes equations

## DOI:

https://doi.org/10.26577/jmmcs-2017-3-477## Keywords:

Cauchy Problem, Stokes equations, inverse problem, FEM, optimization method## Abstract

In this paper we consider the Cauchy problem for the Stokes equations in domain with curvilinear

boundary, the solution is not known on a part of the boundary. This problem is ill-posed. Direct

and conjugate problems are constructed for the initial equations, the definition of generalized

solutions are introduced for these problems in the Sobolev space. It is shown that the solution for

the initial problem is reduced to the solution of the inverse problem for the direct problem. The

inverse problem is represented in operator form, objective functional is constructed, its gradient is

calculated. Computational algorithm is developed for solving the inverse problem for the Stokes

equations on the basis of the combination of optimization method and the finite element method

(FEM).

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## How to Cite

*Journal of Mathematics, Mechanics and Computer Science*,

*95*(3), 78–89. https://doi.org/10.26577/jmmcs-2017-3-477