On a chemotaxis model with nonlinear diffusion modelling multiple sclerosis

We investigated existence of global weak solutions for a system of chemotaxis-hapotaxis type with nonlinear degenerate diffusion arising in modelling multiple sclerosis disease. The model consists of three equations describing the evolution of macrophages (m), cytokine (c) and apoptotic oligodendrocytes (d) densities. The main novelty in our work is the presence of a nonlinear diffusivity D(m), which results to be more appropriate from the modelling point of view. Under suitable assumptions and for sufficiently regular initial data, adapting the strategy in Li and Lankeit (Nonlinearity 29:1564-1595, 2016) and Tao and Winkler (SIAM J Math Anal 43:685-704, 2011), we show the existence of global bounded solutions for the model analysed.