, Volume 99, Issue 1, pp 898-906

Problem of steady motion for a second-grade fluid in the hölder classes of functions

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The paper studies a boundary-value problem (with the usual adherence boundary condition) for a stationary system of equations of motion of second-grade fluids in a bounded domain. This system is not elliptic and contains third-order derivatives of the velocity vector field. This leads to obvious difficulties in the analysis of the problem. It is known that the problem is reduced to the usual Stokes problem and to the transport equations or their analogs. We present a new easier method of such a reduction which allows us to prove the solvability of a stationary boundary-value problem for the equations of motion of second-grade fluids in the Hölder classes of functions in the case of small exterior forces. Bibliography: 6 titles.

Dedicated to the memory of A. P. Oskolkov
Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 243, 1997, pp. 154–168.
Translated by E. V. Frolova.