Well-posedness of aggregation-diffusion systems with irregular kernels
Well-posedness of aggregation-diffusion systems with irregular kernels
We consider aggregation-diffusion equations with merely bounded nonlocal interaction potential $K$. We are interested in establishing their well-posedness theory when the nonlocal interaction potential $K$ is neither differentiable nor positive (semi-)definite, thus preventing application of classical arguments. We prove the existence of weak solutions in two cases: if the mass …