Nonlocal Aggregation Equations and Fluid Dynamics

Andrea Bertozzi
University of California, Los Angeles (UCLA)

This lecture is an introduction to the interesting phenomena of nonlocal aggregation equations and to the open problems in this area. I will review numerical and analytical results for both kinematic and dynamic aggregation equations. I will discuss how models are constructed and the emergence of phenomenological behavior for different types of models including flocking, milling, and other patterns. I will also review some results on well-posedness of aggregation equations including a sharp condition on blowup from smooth initial data. I will talk about connections between these results and classical fluids problems including vortex patches and vortex sheets.

Presentation (PDF File)

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