Recent Developments on Vector Poisson Problems

Abstract: In some physical problems, such as the determination of the vector potential used to represent either the three-dimensional velocity field in incompressible flows or the solenoidal velocity component in transonic potential flows for a compressible fluid as well as the vorticity in three-dimensional viscous incompressible flows, it is necessary to consider a vector field governed by Poisson equation supplemented with various coupling boundary conditions. Recent results on mathematical and numerical analyses of the problems are presented. Some open problems are also proposed.