Seminar| Institute of Mathematical Sciences
Time: Wednesday, June 26th, 2024 , 14:30-15:30
Speaker: Kai Yang, Chongqing University
Abstract: We discuss the asymptotic stability of the solitary waves for the 2d and 3d L2-subcritical Zakharov-Kuznetsov equations. The proof follows the scheme developed by Martel and Merle for the gKdV case. However, compared with the gKdV (as well as the 2d ZK) case, besides establishing the monotone estimates in the multidimensional cases, we also need to overcome two main obstacles: one is the regularity problem for the limit weak solution; the other is the properly selected modulational subspace for the positivity for the Virial operator in the linear Liouville problem. The regularity boost technique is applied for the first obstacle, and the modulational subspace is selected intuitively from our numerical observation. Finally, the positivity of the Virial operator is verified with numerical assistance. This strategy can be extended to all the 2d and 3d L2-subcritical ZK equations, and thus, is considered to be optimal. This is the joint work with Luiz Farah, Justin Holmer and Svetlana Roudenko.