This workshop is part of a series organized through a collaborative research project, a joint NSF-ESRC grant.  The goal is to help develop innovative mathematical methods and techniques to solve some outstanding stability problems of nonlinear partial differential equations across the scales, including asymptotic, quantifying, and structural stability problems in hyperbolic conservation laws, kinetic equations, and related multiscale applications in fluid-particle (agent based) models. A main focus is on the following four interrelated objectives:

•  Stability analysis of shock wave patterns of reflections/diffraction with focus on the shock reflection-diffraction problem in gas dynamics;
• Stability analysis of vortex sheets, contact discontinuities, and other characteristic discontinuities;
• Stability analysis of particle to continuum limits including the quantifying asymptotic/mean-field/large-time limits for pairwise interactions and particle limits for general interactions among multi-agent or many-particle systems;
• Stability analysis of asymptotic limits with emphasis on the vanishing viscosity limit of solutions from multi-dimensional compressible viscous to inviscid flows with large initial data.

We are grateful to the National Science Foundation for supporting the workshop. For any questions please contact either Alexis Vasseur (vasseur@math.utexas.edu) or Ben Seeger (seeger@math.utexas.edu).