## Modern Perspectives in Applied Mathematics: Theory and Numerics of PDEs

### Lagrangian goodies: analyticity and uniqueness

Peter Constantin

Princeton University

Abstract:

The talk is devoted to two results, one about uniqueness of solutions and the other about analyticity of Lagrangian paths for many hydrodynamic models. Uniqueness of solutions of complex hydrodynamic sytems can be difficult to prove in low regularity situations. A Lagrangian description allows a robust uniqueness proof strategy in spaces that guarantee spatial Lipschitz continuity of velocities. In the same class of velocities, in joint work with Vlad Vicol and Jiahong Wu, we prove that particle paths ar real analytic in time.