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

Well-posedness and positivity property for a reaction-diffusion model of plankton communities, involving a rational nonlinearity with singularity