Geodesic
Dirichlet Problem for the Stokes Equation
Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 110-115

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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.
Keywords: flow-through problem, Stokes equation, coercive a priori estimates. 
@article{MZM_2017_101_1_a9,
     author = {V. V. Pukhnachov},
     title = {Dirichlet {Problem} for the {Stokes} {Equation}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {110--115},
     publisher = {mathdoc},
     volume = {101},
     number = {1},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a9/}
}
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V. V. Pukhnachov. Dirichlet Problem for the Stokes Equation. Matematičeskie zametki, Tome 101 (2017) no. 1, pp. 110-115. http://geodesic.mathdoc.fr/item/MZM_2017_101_1_a9/