A mathematical model for phytoplankton

This paper introduces a model of growth and dispersion of the marine phytoplankton, focusing on the effects of the currents (3D) and vertical mixing. Our method consists of describing these effects as the product of the horizontal current, which is solved along the characteristic lines, and the coupled action of vertical current and vertical diffusion, restricted on each characteristic line of the horizontal current. We show that the trivial steady state loses its stability and a nontrivial (non-constant in space) steady state is created.