A class of large amplitude oscillating solutions for three dimensional Euler equations

International audienceIn this article, we construct large amplitude oscillating waves, noted (uε)ε where ε∈]0,1] is a parameter going to zero, which are devised to be local solutions on some open domain of the time-space R+×R3 of both the three dimensional Burger equations (without source term), the compressible Euler equations (with some constant pressure) and the incompressible Euler equations (without pressure). The functions uε(t,x) are characterized by the fact that the corresponding Jacobian matrices Dxuε(t,x) are nilpotent of rank one or two. Our purpose is to describe the interesting geometrical features of the expressions uε(t,x) which can be obtained by this way