TY - JOUR

T1 - Dirichlet problem for the Stokes equation

AU - Pukhnachev, V. V.

PY - 2017/1/1

Y1 - 2017/1/1

N2 - The paper presents some coercive a priori estimates of the solution of the Dirichlet problem for the linear Stokes equation relating vorticity and the stream function of an axially symmetric flow of an incompressible fluid. This equation degenerates on the axis of symmetry. The method used to obtain the estimates is based on a differential substitution transforming the Stokes equation into the Laplace equation and on the subsequent transition from cylindrical to Cartesian coordinates in three-dimensional space.

AB - The paper presents some coercive a priori estimates of the solution of the Dirichlet problem for the linear Stokes equation relating vorticity and the stream function of an axially symmetric flow of an incompressible fluid. This equation degenerates on the axis of symmetry. The method used to obtain the estimates is based on a differential substitution transforming the Stokes equation into the Laplace equation and on the subsequent transition from cylindrical to Cartesian coordinates in three-dimensional space.

KW - coercive a priori estimates

KW - flow-through problem

KW - Stokes equation

UR - http://www.scopus.com/inward/record.url?scp=85015698840&partnerID=8YFLogxK

U2 - 10.1134/S0001434617010138

DO - 10.1134/S0001434617010138

M3 - Article

AN - SCOPUS:85015698840

VL - 101

SP - 132

EP - 136

JO - Mathematical Notes

JF - Mathematical Notes

SN - 0001-4346

IS - 1-2

ER -