On the Navier-Stokes equations with free convection in three-dimensional unbounded triangular channels

The quaternionic calculus is a powerful tool for treating the Navier-Stokes equations very elegantly and in a compact form, through the evaluation of two types of integral operators: the Teodorescu operator and the quaternionic Bergman projector. While the integral kernel of the Teodorescu transform is universal for all domains, the kernel function of the Bergman projector, called the Bergman kernel, depends on the geometry of the domain. In this paper, we use special variants of quaternionic-holomorphic multiperiodic functions in order to obtain explicit formulas for unbounded three-dimensional parallel plate channels, rectangular block domains and regular triangular channels.