One problem of the Navier type for the Stokes system in planar domains (Q324576)

The principal result of this work is the reduction of the system defined as NEWLINE\[NEWLINE \Delta\mathbf{n}+\nabla \rho=\mathbf{F},\, \nabla\cdot\mathbf{u}=G\,\text{ in }\Omega NEWLINE\]NEWLINE NEWLINE\[NEWLINE \mathbf{u}\cdot\vec{\tau}=g,\,\rho=h\,\text{ on }\partial\Omega NEWLINE\]NEWLINE to the Dirichlet and Neumann problems for the Laplace equation that allows the proof of uniqueness of the solution for the original system and study of its regularity by methods of complex analysis.