4 papers
math.AP2026
Construction of two-bubble blow-up solutions for the mass-critical gKdV equations
Yang Lan, Xu Yuan
For the mass-critical generalized Korteweg-de Vries equation, We…
math.AP2026
Asymptotic stability of smooth solitons and multi-solitons for the Camassa--Holm equation
Robin Ming Chen, Yang Lan, Yue Liu +1
We establish the asymptotic stability of smooth solitons and multi-solitons for the Camassa-Holm (CH) equation in the energy space . We show that solutions initially close…
math.AP2025
Construction of blow-up solution with minimal mass for 2D cubic Zakharov--Kuznetsov equation
Yang Lan, Xu Yuan
In this article, we construct a minimal mass blow-up solution of the two-dimensional cubic (mass-critical) Zakharov--Kuznetsov equation: \begin{equation*} \partial_t Ï+\partial_{x…
math.AP2024
Nonexistence of minimal mass blow-up solution for the 2D cubic Zakharov-Kuznetsov equation
Gong Chen, Yang Lan, Xu Yuan
For the 2D cubic (mass-critical) Zakharov-Kuznetsov equation, \begin{equation*} \partial_tÏ+\partial_{x_1}(ÎÏ+Ï^3)=0,\quad (t,x)\in [0,\infty)\times \mathbb{R}^{2}, \end{equati…