Existence and large time behavior in hydrodynamic swarming

I will discuss recent developments in our study of hydrodynamic swarming driven by symmetric communication kernels. A main question of interest is the emergent behavior which we quantify in terms of the spectral gap of a weighted Laplacian associated with the alignment operator. I will derive threshold conditions which guarantee existence of multiD strong solutions, their large time flocking behavior with long-range kernels, and mention open questions for in the presence of short-range kernels.