Dirichlet problems for disk of the meridian plane (Q2739823)

The basis characteristics of the solenoidal potential field with axial symmetry in its meridian plane are the potential \(\varphi(x,y)\) and the Stokes flow function \(\psi(x,y)\) satisfying the equations NEWLINE\[NEWLINEy\Delta\varphi (x,y)+ {{\partial\varphi}\over{\partial y}}=0,\;y\Delta \psi(x,y)-{{\partial\psi}\over {\partial y}}=0.NEWLINE\]NEWLINE The author gives effective methods for solving the Dirichlet problems for \(\varphi(x,y)\) and \(\psi(x,y)\) which are adopted for the meridian plane. New integral representations of the solutions allow to use methods of singular integral equations for the solution of the boundary value problems in the meridian plane.