Asymptotic Stability of solitons of the high dimensional Zakharov-Kuznetsov equation

16h

Claudio Muñoz (DIM-CMM)

Asymptotic Stability of solitons of the high dimensional Zakharov-Kuznetsov equation

In this talk I will discuss a recent work with R. Cote, D. Pilod and G. Simpson, where we considered solitons of the high dimensional Zakharov-Kuznetsov equation, a model of plasma ions in Physics. In particular, we prove that solitons are strongly asymptotically stable in the energy space, in a particular region of the plane determined by natural geometric and dispersive constraints. In proving this result we extend to the high dimensional case several tools coming from the one-dimensional setting (generalized KdV equations), introduced by Martel and Merle. However, some new difficulties arise when consider the dimension greater than two, in particular when proving required spectral properties, decay estimates, and the compactness in time of the asymptotic solution.