4 papers · 1 filter
Scattering of the 3D Zakharov-Kuznetsov equation
Philippe Anjolras
We consider the Zakharov-Kuznetsov equation in space dimension 3: \[ \left\{ \begin{array}{l} \partial_t u + \partial_x Îu + \partial_x \frac{u^2}{2} = 0 \\ u(t = 0) = u_0 \end{ar…
Scattering of the 2D modified Zakharov-Kuznetsov equation
Philippe Anjolras
We study the modified Zakharov-Kuznetsov equation in dimension : \[ \partial_t u + \partial_x \left( Îu + u^3 \right) = 0 \] where $u : (t, (x, y)) \in \mathbb{R} \times \math…
Path-connectedness of incompressible Euler solutions
Philippe Anjolras
We study the incompressible Euler equation and prove that the set of weak solutions is path-connected. More precisely, we construct paths of Hölder regularity , valued in…
Stability of the constant states in the augmented Born-Infeld system
Philippe Anjolras
In this paper, we consider the Born-Infeld system, arising as a nonlinear model of electromagnetism, and its extension introduced by Brenier [Bre04] the so-called "augmented Born-I…