5 papers
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…
Well-posedness, mean attractors and invariant measures of stochastic discrete long-wave-short-wave resonance equations driven by locally Lipschitz nonlinear noise
Xia Pan, Jianhua Huang, Juntao Wu +1
This paper is devoted to investigating the random dynamics of stochastic discrete long-wave-short-wave resonance equations, which are characterized by the following features: …
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…
Strichartz estimates for orthonormal functions and probabilistic convergence of density functions of compact operators on manifolds
Wei Yan, Jinqiao Duan, Jianhua Huang +2
In this paper, we establish some Strichartz estimates for orthonormal functions and probabilistic convergence of density functions related to compact operators on manifolds. Firstl…
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)…