The Cauchy problem for the Stokes equations - Dairbayeva, G. (Journal of Mathematics, Mechanics and Computer Science, 2018)
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).