Large amplitude oscillating solutions for three dimensional incompressible Euler equations

Christophe Cheverry (1) , Mekki Houbad (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

In this article, we construct large amplitude oscillating waves which are local solutions on some open domain of the time-space of both the three dimensional Burger equations (without source term) and the incompressible Euler equations (without pressure). The solutions are mainly characterized by the fact that the corresponding Jacobian matrices are nilpotent of rank one or two. Our purpose here is to describe the interesting geometrical features of the expressions obtained by this way.

Mots clés: Hyperbolic systems; Oscillations; Burger; Euler

Domaines: Equations aux dérivées partielles [math.AP]

Christophe Cheverry, Mekki Houbad. Large amplitude oscillating solutions for three dimensional incompressible Euler equations. 2010. ⟨hal-00512687⟩