2 citations · 7 across the 12 of their papers we have counts for
13 papers
Feynman-Kac Representation and the Asymptotic Speed of the Fisher-KPP Equation with Finite-Activity Jump Noise
Yuhong Li, Hao Wen, Jianhua Huang
We study the asymptotic propagation speed of travelling wave solutions to the stochastic Fisher--KPP equation with multiplicative finite-activity pure jump Lévy noise, i.e.\ a comp…
Mean-square invariant manifolds for ill-posed stochastic evolution equations driven by nonlinear noise
Zonghao Li, Caibin Zeng, Jianhua Huang
This paper discerns the invariant manifold of a class of ill-posed stochastic evolution equations driven by a nonlinear multiplicative noise. To be more precise, we establish the e…
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…
Exponential mixing for the fractional Magneto-Hydrodynamic equations with degenerate stochastic forcing
Xuhui Peng, Jianhua Huang, Yan Zheng
We establish the existence, uniqueness and exponential attraction properties of an invariant measure for the MHD equations with degenerate stochastic forcing acting only in the mag…
Ergodicity and exponential mixing of the real Ginzburg-Landau equation with a degenerate noiss
Xuhui Peng, Jianhua Huang, Rangrang Zhang
In this paper, we establish the existence, uniqueness and attraction properties of an invariant measure for the real Ginzburg-Landau equation in the presence of a degenerate stocha…
New lower bounds on the radius of spatial analyticity for the KdV equation
Jianhua Huang, Ming Wang
The radius of spatial analyticity for solutions of the KdV equation is studied. It is shown that the analyticity radius does not decay faster than as time goes to in…
The Cauchy problem for two dimensional generalized Kadomtsev-Petviashvili-I equation in anisotropic Sobolev spaces
Wei Yan, Yongsheng Li, Jianhua Huang +1
The goal of this paper is three-fold. Firstly, we prove that the Cauchy problem for generalized KP-I equation \begin{eqnarray*} u_{t}+|D_{x}|^α\partial_{x}u+\partial_{x}^{-1}\parti…
Random data Cauchy problem for a generalized KdV equation in the supercritical case
Wei Yan, Jinqiao Duan, Jianhua Huang
We consider the Cauchy problem for a generalized KdV equation \begin{eqnarray*} u_{t}+\partial_{x}^{3}u+u^{7}u_{x}=0, \end{eqnarray*} with random data on \R. Kenig, Ponce, Vega(Com…
Random data Cauchy problem for the wave equation on compact manifold
Jinqiao Duan, Jianhua Huang, Yongsheng Li +1
Inspired by the work of Burq and Tzvetkov (Invent. math. 173(2008), 449-475.), firstly, we construct the local strong solution to the cubic nonlinear wave equation with random data…
Sharp well-posedness and ill-posedness of the Cauchy problem for the higher-order KdV
Wei Yan, Minjie Jiang, Yongsheng Li +1
In this paper, we investigate the Cauchy problem for the higher-order KdV-type equation \begin{eqnarray*} u_{t}+(-1)^{j+1}\partial_{x}^{2j+1}u + \frac{1}{2}\partial_{x}(u^{2}) = 0,…
Well-posedness for Stochastic Generalized Fractional Benjamin-Ono Equation
Wei Yan, Jianhua Huang, Boling Guo
This paper is devoted to the Cauchy problem for the stochastic generalized Benjamin-Ono equation. By using the Bourgain spaces and Fourier restriction method and the assumption tha…
The Cauchy problem for the Ostrovsky equation with negative dispersion at the critical regularity
Yongsheng Li, Jianhua Huang, Wei Yan
In this paper, we investigate 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) -γu=…
Dynamics of stochastic non-Newtonian fluids driven by fractional Brownian motion with Hurst parameter
Jin Li, Jianhua Huang
In this paper we consider the Stochastic isothermal, nonlinear, incompressible bipolar viscous fluids driven by a genuine cylindrical fractional Bronwnian motion with Hurst paramet…