10 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…
Spatial decay and nonlinear smoothing of the sixth-order Boussinesq equation
Xiangqian Yan, Yongsheng Li, Wei Yan
In this paper, we study the initial value problem of the sixth-order Boussinesq equation with quadratic and cubic nonlinearities in arbitrary spatial dimensions. First, by using th…
Spatial decay and nonlinear smoothing of the generalized Ostrovsky equation
Xiangqian Yan, Wei Yan, Meihua Yang
This paper is devoted to studying the generalized Ostrovsky equation \begin{eqnarray*} u_{t}-β\partial_{x}^{3}u-γ\partial_{x}^{-1}u+\frac{1}{k+1}(u^{k+1})_{x}=0,k\geq5 \end{eqnarra…
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…
The probabilistic convergence problem of density functions related to
Xiangqian Yan, Yongsheng Li, Wei Yan
In this article, by using full randomization introduced by Hadama and Yamamoto (Probabilistic Strichartz estimates in Schatten classes and their applications to Hartree equation, J…
Strichartz estimates for orthonormal functions and convergence problem of density functions of Boussinesq operator on manifolds
Xiangqian Yan, Yongsheng Li, Wei Yan +1
This paper is devoted to studying the maximal-in-time estimates and Strichartz estimates for orthonormal functions and convergence problem of density functions related to Boussines…
Convergence problem of the Kawahara equation on the real line
Wei Yan, Weimin Wang, Xiangqian Yan
In this paper, we consider the convergence problem of the Kawahara equation \begin{eqnarray*} &&u_{t}+α\partial_{x}^{5}u+β\partial_{x}^{3}u+\partial_{x}(u^{2})=0 \end{eqnarray*} on…
The Cauchy problem for the generalized Ostrovsky equation with negative dispersion
Xiangqian Yan, Wei Yan
This paper is devoted to studying the Cauchy problem for the generalized Ostrovsky equation \begin{eqnarray*} u_{t}-β\partial_{x}^{3}u-γ\partial_{x}^{-1}u+\frac{1}{k+1}(u^{k+1})_{x…
Convergence problem of Schrödinger equation in Fourier-Lebesgue spaces with rough data and random data
Xiangqian Yan, Yajuan Zhao, Wei Yan
In this paper, we consider the convergence problem of Schrödinger equation. Firstly, we show the almost everywhere pointwise convergence of Schrödinger equation in Fourier-Lebesgue…
The Cauchy problem for the generalized KdV equation with rough data and random data
Wei Yan, Xiangqian Yan, Jinqiao Duan +1
In this paper, we consider the Cauchy problem for the generalized KdV equation with rough data and random data. Firstly, we prove that as $t\longrigh…