8 citations · 29 across the 25 of their papers we have counts for
25 papers
A perturbation result for the energy critical Choquard equation in
Xinyu Bo, Guangying Lv, Xingdong Tang +1
We study the singularly perturbed nonlinear energy critical Choquard equation \begin{equation*} -{\Laplace u}\qty({x}) -α \int_{\R^N}\frac{u^p\qty(y)}{\abs{x-y}^λ}\odif{y} u^{p-1}\…
Stochastic transport equation with bounded and Dini continuous drift
Jinlong Wei, Guangying Lv, Wei Wang
The results established by Flandoli, Gubinelli and Priola ({\it Invent. Math.} {\bf 180} (2010) 1--53) for stochastic transport equation with bounded and Hölder continuous drift ar…
Noise and Stability in Reaction-diffusion Equations
Guangying Lv, Jinlong Wei, Guang-an Zou
We study the stability of reaction-diffusion equations in presence of noise. The relationship of stability of solutions between the stochastic ordinary different equations and the…
A Kolmogorov type theorem for stochastic fields
Jinlong Wei, Guangying Lv
We generalize the Kolmogorov continuity theorem and prove the continuity of a class of stochastic fields with the parameter. As an application, we derive the continuity of solution…
Impact of noise on parabolic equations
Guangying Lv, Jinlong Wei
In this short paper, we focus on the blowup phenomenon of stochastic parabolic equations. We first discuss the probability of the event that the solutions keep positive. Then, the…
Schauder and Sobolev Estimates of Parabolic Equations
Guangying Lv, Jinlong Wei
In this note, we use the non-homogeneous Poisson stochastic process to show how knowing Schauder and Sobolev estimates for the one-dimensional heat equation allows one to derive th…
Blowup solutions for stochastic parabolic equations
G. Lv, J. Wei
In this short paper, we are concerned with the blowup phenomenon of stochastic parabolic equations. By using comparison principle and the results of deterministic parabolic equatio…
Blowup solutions of Grushin's operator
Guangying Lv, Jinlong Wei, Longjie Xie
In this note, we consider the blowup phenomenon of Grushin's operator. By using the knowledge of probability, we first get expression of heat kernel of Grushin's operator. Then by…
Global existence and non-existence of stochastic parabolic equations
Guangying Lv, Jinlong Wei
This paper is concerned with the blowup phenomenon of stochastic parabolic equations both on bounded domain and in the whole space. We introduce a new method to study the blowup ph…
Periodic solution of stochastic process in the distributional sense
Guangying Lv, Hongjun Gao, Jinlong Wei
In this paper, we aim to study a stochastic process from a macro point of view, and thus periodic solution of a stochastic process in distributional sense is introduced. We first g…
The effect of noise intensity on stochastic parabolic equations
Guangying Lv, Hongjun Gao, Jinlong Wei +1
In the present paper, the effect of noise intensity on stochastic parabolic equations is discussed. We focus on the effect of noise on the energy solutions of the stochastic parabo…
Regularity of stochastic nonlocal diffusion equations
Guangying Lv, Hongjun Gao, Jinlong Wei +1
In this paper, we are concerned with regularity of nonlocal stochastic partial differential equations of parabolic type. By using Companato estimates and Sobolev embedding theorem,…
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 …
On weak solutions of stochastic differential equations with sharp drift coefficients
Jinlong Wei, Guangying Lv, Jiang-Lun Wu
We extend Krylov and Röckner's result \cite{KR} to the drift coefficients in critical Lebesgue space, and prove the existence and uniqueness of weak solutions for a class of SDEs.…
Stochastic Navier-Stokes equations with Caputo derivative driven by fractional noises
Guang-an Zou, Guangying Lv, Jiang-Lun Wu
In this paper, we consider the extended stochastic Navier-Stokes equations with Caputo derivative driven by fractional Brownian motion. We firstly derive the pathwise spatial and t…
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…
Schauder estimates for stochastic transport-diffusion equations with Lévy processes
Jinlong Wei, Jinqiao Duan, Guangying Lv
We consider a transport-diffusion equation with Lévy noises and Hölder continuous coefficients. By using the heat kernel estimates, we derive the Schauder estimates for the mild so…
Morrey-Campanato estimates for the moments of stochastic integral operators and its application to SPDEs
Guangying Lv, Hongjun Gao, Jinlong Wei +1
In this paper, we are concerned with the estimates for the moments of stochastic convolution integrals. We first deal with the stochastic singular integral operators and we aim to…
BMO estimates for stochastic singular integral operators and its application to PDEs with Lévy noise
Guangying Lv, Hongjun Gao, Jinlong Wei +1
In this paper, we consider the stochastic singular integral operators and obtain the BMO estimates. As an application, we consider the fractional Laplacian equation with additive n…
Kinetic solutions for nonlocal stochastic conservation laws
Lv Guangying, Gao Hongjun, Wei Jinlong
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 and…
Well-posedness of nonlinear transport equation by stochastic perturbation
Jinlong Wei, Rongrong Tian, Guangying Lv
We are concerned with multidimensional nonlinear stochastic transport equation driven by Brownian motions. For irregular fluxes, by using stochastic BGK approximations and commutat…
A regularity result for the nonlocal Fokker-Planck equation with Ornstein-Uhlenbeck drift
Xiaoxia Xie, Jinqiao Duan, Xiaofan Li +1
Despite there are numerous theoretical studies of stochastic differential equations with a symmetric -stable Lévy noise, very few regularity results exist in the case of $0<α\le…
Martingale and Weak Solutions for a Stochastic Nonlocal Burgers Equation on Bounded Intervals
Guangying Lv, Jinqiao Duan
This work is about the existence of martingale solutions and weak solutions for a stochastic nonlocal Burgers equation on bounded intervals. The existence of a martingale solution…