Singular Solutions and Pattern Formation in Aggregation Equations
Dr. Hui Sun
Department of Mathematics and Center for Theoretical Biological Physics
UC San Diego
In this work, we study singular solutions and pattern formation in aggregation swarming models in two dimensions. This class of models involve pairwise interactions and an active scalar equation in the continuum limit. We show the connection between this model and the classical vorticity equation from fluid dynamics. The aggregation model can lead to a rich family of patterns. We discuss the stability of the singular patterns formed with this model.