Zusammenfassung für den Vortrag am 10.05.2016 (15:15 Uhr)

Oberseminar ANALYSIS - PROBABILITY

Nicolas Besse (Université Côte d'Azur)
A constructive approach to regularity of Lagrangian trajectories for incompressible Euler flow in a bounded domain

We give a constructive proof of smoothness (in ultradifferentiable classes) of Lagrangian trajectories for 3D incompressible Euler flows in an impermeable bounded domain

whose boundary is ultradifferentiable, i.e. may be either

analytic or have a regularity between indefinite differentiability

and analyticity. Based on a little-known Cauchy Lagrangian formulation of the 3D incompressible Euler equations, we establish novel explicit recursion relations that include contributions from the boundary.

This leads to a constructive proof of time-analyticity of the Lagrangian

trajectories with analytic boundaries, which can then be used

subsequently for the design of a very high-order Cauchy-Lagrangian method

to study numerically, among other, the open issue of finite time blow up of classical solutions.