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math.AP2026
Almost sure spatial decay and almost sure nonlinear smoothing of some stochastic dispersive equations
Xiangqian Yan, Yongsheng Li, Jianhua Huang +1
In this paper, we consider the almost sure nonlinear smoothing, the almost sure spatial decay and the almost sure uniform convergence of the stochastic mKdV equation and the stocha…
math.AP2026
The Cauchy problem for the generalized KdV equation in the Sobolev space
Xiangqian Yan, Yongsheng Li, Juan Huang +2
In this paper, we are concerned with the Cauchy problem for the generalized KdV equation with random data and rough data. Firstly, when , by using the initial value…
math.AP2015
The Cauchy problem for the Ostrovsky equation with positive dispersion
Wei Yan, Yongsheng Li, Jianhua Huang +1
This paper is devoted to studying the Cauchy problem for the Ostrovsky equation \begin{eqnarray*} \partial_{x}\left(u_{t}-β\partial_{x}^{3}u +\frac{1}{2}\partial_{x}(u^{2})\right)…