Abstract
A time-periodic Stokes problem is studied in the domain with cylindrical outlets to infinity. Using the Fourier series the problem is reduced to a sequence of elliptic problem. For each of these elliptic boundary value problems a generalized Green’s formula is constructed. The analogous Green’s formula for the steady Stokes problem was obtained in [1].
Highlights
Let ⊂ R3 be a domain with cylindrical outlets to infinity, i.e., outside the ball BR = x ∈ R3: |x| R the domain coincides with a system of J semi-infinite cylinders j +
Inserting series (5), (6) into equations and boundary conditions we get for coefficients vck, vsk, pck, psk series of the systems of elliptic problems kvsk − ν −kvck −
Let xj = (x1j, x2j, x3j ) be the local coordinate system related to the cylinder j +
Summary
Inserting series (5), (6) into equations and boundary conditions we get for coefficients vck, vsk, pck, psk series of the systems of elliptic problems kvsk − ν −kvck − In this paper we derive so-called generalized Green’s formula for problem (7). The analogous Green’s formula for the steady Stokes problem was obtained in [1].
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