  In this note we prove the existence and uniqueness of weak solutions for the
boundary value problem modelling the stationary case of the bioconvective flow
problem introduced by Tuval et. al. (2005, {\it PNAS} 102, 2277--2282). We
derive some appropriate a priori estimates for the weak solution, which implies
the existence, by application of Gossez theorem, and the uniqueness by standard
methodology of comparison of two arbitrary solutions.
