Analyticity of Lagrangian trajectories for well posed inviscid incompressible fluid models

Understand

We discuss general incompressible inviscid models, including the Euler equations, the surface quasi-geostrophic equation, incompressible porous medium equation, and Boussinesq equations.

• All these models have classical unique solutions, at least for short time.
• We show that they have real analytic Lagrangian paths.
• More precisely, we show that as long as a solution of any of these equations is in a class of regularity that assures H\"{o}lder continuous gradients of velocity, the corresponding Lagrangian paths are real analytic functions of time.