  In this work, we consider a reaction-diffusion system, modeling the
interaction between nutrients, phytoplanktons and zooplanktons. Using a
semigroup approach in $L^2$, we prove global existence, uniqueness and
positivity of the solutions. The Holling type 2 nonlinearities, i.e of rational
type with singularity, are handled by providing estimates in $L^\infty$. The
article finally exhibits some time asymptotics properties of the solutions.
