Abstract for the talk at 10.02.2010 (15:15 h)

Isabelle Greff (Université de Pau et des Pays de l'Adour, Laboratoire de Mathématiques Appliquées IPRA, Pau, France)

Non-differentiable embedding of Lagrangian systems and partial differential equations

We develop the non-differentiable embedding theory of differential operators and Lagrangian systems using a new operator on non-differentiable functions. We then construct the corresponding calculus of variations and we derive the associated non-differentiable Euler-Lagrange equation, and apply this formalism to the study of PDE's. We extend the characteristics method to the non-differentiable case. We prove that non-differentiable characteristics for the Navier-Stokes equation correspond to extremals of an explicit non-differentiable Lagrangian system.