On the Boundary Integral Equations for a Two-Dimensional Slowly Rotating Highly Viscous Fluid Flow (Advances in Applied Mathematics and Mechanics, 2018)
In this paper, the two-dimensional slowly rotating highly viscousfluid flow in small cavities is modelled by the triharmonic equationfor the streamfunction.  The Dirichlet problem for this triharmonicequation is recast as a set of three boundary integral equationswhich however, do not have a unique solution for three exceptionalgeometries of the boundary curve surrounding the planar solutiondomain.  This defect can be removed either by using modifiedfundamental solutions or by adding two supplementary boundaryintegral conditions which the solution of the boundary integralequations must satisfy. The analysis is further generalized topolyharmonic equations.