An Arbitrary Lagrangian Eulerian formulation for a 3D eutrophication model in a moving domain

This work analyzes a realistic mathematical model that governs eutrophication (an ecological process involving nutrients, phytoplankton, zooplankton, organic detritus and dissolved oxygen) into a moving aquatic domain. As a main result, we obtain existence-uniqueness results for the solution of the system within the general framework of non-cylindrical domains (based on studying the properties of a generic parabolic problem). The fact of dealing with moving domains, and the lack of regularity, preclude the use of standard semigroup approach, forcing us towards the utilization of Arbitrary Lagrangian Eulerian techniques.