High-friction limit for bipolar Euler-Riesz systems

Abstract: We consider a bipolar Euler-Riesz system and rigorously justify the high-friction limit of weak solutions towards a bipolar aggregation-diffusion system with Riesz interactions. The analysis is carried out via the relative entropy method in the regime where smooth solutions of the limiting equations exist. This extends previous results on the high-friction limit of bipolar Euler-Poisson systems to a more general class of interactions, and extends the one-species Euler-Riesz case to the bipolar setting.