Boundedness in a Biofilm-Chemotaxis Model in Evolving Porous Media

Abstract

The article concerns with a model discribing the growth of a biofilm made by chemotactical bacteria within a saturated porous media and affects the flow through the pores. The underlying model describing this process on the macroscale is derived in [21]. Therein also solvability in a weak sense and boundedness of solutions with high regularity is investigated. This current paper verifies the existence of bounded weak solutions in case of less regularity assumptions on the data.