Global Existence for Reaction-Diffusion Systems with Mass Control and Critical Growth with Respect to the Gradient1

In this paper we study the existence of global weak solutions for 2 2 reactiondiffusion systems for which two main properties hold: the positivity of the solutions and the total mass of the components are preserved with time. Moreover we suppose that the non-linearities have critical growth with respect to the gradient. The technique we use here in order to prove global existence is in the same spirit of the method developed by Boccardo, Murat, and Puel for a single equation