182 citations · 1.5k across the 227 of their papers we have counts for
41 papers · 1 filter
Entropy Production and Reversibility Criteria for Stochastic Evolution Equations
Jinqiao Duan, Ao Zhang, Johannes Zimmer
This paper develops a path-space theory of entropy production for a class of stochastic evolution equations on infinite-dimensional Hilbert spaces. Since such spaces have no canoni…
Stochastic Perturbations in the Fractional Nonlinear Schrödinger Equation: Well-posedness and Blow-up
Ao Zhang, Yanjie Zhang, Jinqiao Duan
This work investigates radial solutions for nonlinear fractional Schrödinger equations driven by multiplicative noise. Leveraging radial deterministic and stochastic Strichartz est…
Perturbation of the spectra for asymptotically constant differential operators and applications
Shuang Chen, Jinqiao Duan
We study the spectra for a class of differential operators with asymptotically constant coefficients.These operators widely arise as the linearizations of nonlinear partial differe…
Effective Approximation for a Stochastic System with Large Potential
Ao Zhang, Jinqiao Duan
This letter is about effective approximation for a stochastic parabolic equation with a large potential in a periodic medium. Under a condition on the spectral properties of the as…
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…
Sharp well-posedness of the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili equation in anisotropic Sobolev spaces
Wei Yan, Yimin Zhang, Yongsheng Li +1
We consider the Cauchy problem for the rotation-modified Kadomtsev-Petviashvili (RMKP) equation \begin{align*} \partial_{x}\left(u_{t}-β\partial_{x}^{3}u +\partial_{x}(u^{2})\right…
Pointwise convergence problem of Ostrovsky equation with rough data and random data
Wei Yan, Qiaoqiao Zhang, Jinqiao Duan +1
In this paper, we consider the pointwise convergence problem of free Ostrovsky equation with rough data and random data. Firstly, we show the almost everywhere pointwise convergenc…
Effective Wave Factorization for a Stochastic Schrödinger Equation
Ao Zhang, Jinqiao Duan
We study the homogenization of a stochastic Schrödinger equation with a large periodic potential in solid state physics. Denoting by the period, the potential is scal…
Probabilistic pointwise convergence problem of some dispersive equations
Wei Yan, Jinqiao Duan, Yongsheng Li +1
In this paper, we investigate the almost surely pointwise convergence problem of free KdV equation, free wave equation, free elliptic and non-elliptic Schrödinger equation respecti…
Global Solution and Blow-up of the Stochastic Nonlinear Schrödinger system
Qi Zhang, Jinqiao Duan, Yong Chen
We study the stochastic Nonlinear Schrödinger system with multiplicative white noise in energy space . Based on deterministic and stochastic Strichartz estimates, we prove the…
Recurrent Solutions of a Nonautonomous Modified Swift-Hohenberg Equation
Jintao Wang, Lu Yang, Jinqiao Duan
We consider recurrent solutions of the nonautonomous modified Swift-Hohenberg equation We employ Conley index theory to show that, if…
Slow manifolds for a nonlocal fast-slow stochastic evolutionary system with stable Levy noise
Hina Zulfiqar, Shenglan Yuan, Ziying He +1
This work aims at understanding the slow dynamics of a nonlocal fast-slow stochastic evolutionary system with stable Levy noise. Slow manifolds along with exponential tracking prop…
Homogenization of Nonlocal Partial Differential Equations Related to Stochastic Differential Equations with Lévy Noise
Qiao Huang, Jinqiao Duan, Renming Song
We study the "periodic homogenization" for a class of nonlocal partial differential equations of parabolic-type with rapidly oscillating coefficients, related to stochastic differe…
Strong solution for stochastic transport equations with irregular drift: existence and non-existence
Jinlong Wei, Jinqiao Duan, Hongjun Gao +1
We prove some existence, uniqueness and non-existence results of stochastic strong solutions for a class of stochastic transport equations with a -integrable (in time), bounded…
Existence and uniqueness of -solutions for stochastic transport equations
Jinlong Wei, Jinqiao Duan, Hongjun Gao +1
We investigate a stochastic transport equation driven by a multiplicative noise. For drift coefficient and …
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…
Kinetic solutions for nonlocal scalar conservation laws
Jinlong Wei, Jinqiao Duan, Guangying Lv
This work is devoted to examine the uniqueness and existence of kinetic solutions for a class of scalar conservation laws involving a nonlocal super-critical diffusion operator. Ou…
Maximum principles for nonlocal parabolic Waldenfels operators
Qiao Huang, Jinqiao Duan, Jiang-Lun Wu
As a class of Lévy type Markov generators, nonlocal Waldenfels operators appear naturally in the context of investigating stochastic dynamics under Lévy fluctuations and constructi…
Approximation of the inertial manifold for a nonlocal dynamical system
Xingjie Yan, Jinchun He, Jinqiao Duan
We consider inertial manifolds and their approximation for a class of partial differential equations with a nonlocal Laplacian operator , with . The nonlo…
Impacts of Noise on a Class of Partial Differential Equations
Guangying Lv, Jinqiao Duan
This paper is concerned with effects of noise on the solutions of partial differential equations. We first provide a sufficient condition to ensure the existence of a unique positi…
Global solutions for a nonlocal Ginzberg-Landau equation and a nonlocal Fokker-Plank equation
Jinchun He, Jinqiao Duan, Hongjun Gao
This work is devoted to the study of a nonlocal Ginzberg-Landau equation by the semigroup method and a nonlocal Fokker-Plank equation by the viscosity vanishing method. For the non…
Slow foliation of a slow-fast stochastic evolutionary system
Guanggan Chen, Jinqiao Duan, Jian Zhang
This work is concerned with the dynamics of a slow-fast stochastic evolutionary system quantified with a scale parameter. An invariant foliation decomposes the state space into geo…