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Vanishing viscosity asymptotics for Stokes equations.

This paper deals with the properties of solutions to initial–boundary value problems for the nonstationary Stokes equations with vanishing viscosity in a bounded three-dimensional domain. We determine the initial terms in asymptotic expansions of solutions at vanishing viscosity and give error estimates for such approximate expansions. The study of the properties of solutions to fluid dynamics problems with vanishing viscosity is a well-known problem with a long history, and there are methods developed for analyzing this problem (boundary layer theory). However, a rigorous mathematical approach to this problem has apparently been developed only for initial–boundary value problems associated with the nonstationary Navier–Stokes equations in a bounded two-dimensional domain under additional assumptions on the asymptotic behavior of solutions to this problem (further details and rigorous statements can be found in [1]).



Taras Shevchenko National University of Kyiv

Gennadiy Sandrakov