9 papers
Global well-posedness of the energy-critical nonlinear Schrödinger equation on the three-dimensional torus with additive Lévy noise
Bin Liu, Fan Xu
This paper establishes global well-posedness for the defocusing energy-critical nonlinear Schrödinger equation on the three-dimensional torus with a class of additive Lévy noises.…
Well-posedness of the Stochastic Landau--Lifshitz--Baryakhtar Equation in
Bin Liu, Fan Xu
This paper studies the Cauchy problem for the stochastic Landau--Lifshitz--Baryakhtar equation on , , subject to Stratonovich Gaussian perturbations. We esta…
Existence and uniqueness of global large-data solutions for the Chemotaxis-Navier-Stokes system in
Fan Xu, Bin Liu
This work investigates the Cauchy problem for the classical Chemotaxis-Navier-Stokes (CNS) system in . We establish the global existence and uniqueness of strong, cla…
Global well-posedness for the Landau-Lifshitz-Baryakhtar equation in
Fan Xu, Bin Liu
This paper establishes the global well-posedness of the Landau-Lifshitz-Baryakhtar (LLBar) equation in the whole space . The study first demonstrates the existence an…
Global strong solution for the stochastic tamed Chemotaxis-Navier-Stokes system in
Fan Xu, Lei Zhang, Bin Liu
In this work, we consider the 3D Cauchy problem for a coupled system arising in biomathematics, consisting of a chemotaxis model with a cubic logistic source and the stochastic tam…
A chemotaxis-fluid model driven by Lévy noise in
Fan Xu, Lei Zhang, Bin Liu
In this paper, we investigate the existence and uniqueness of global solutions to the Cauchy problem for a coupled stochastic chemotaxis-Navier-Stokes system with multiplicative Lé…
Well-posedness and large deviations of Lévy-driven Marcus stochastic Landau-Lifshitz-Baryakhtar equation
Fan Xu, Bin Liu, Lei Zhang
This paper considers the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with pure jump noise in Marcus canonical form, which describes the dynamics of magnetic spin field…
Well-posedness and invariant measures for the stochastically perturbed Landau-Lifshitz-Baryakhtar equation
Fan Xu, Lei Zhang, Bin Liu
In this paper, we study the initial-boundary value problem for the stochastic Landau-Lifshitz-Baryakhtar (SLLBar) equation with Stratonovich-type noise in bounded domains $\mathcal…
New global Carleman estimates and null controllability for forward/backward semi-linear parabolic SPDEs
Lei Zhang, Fan Xu, Bin Liu
In this paper, we study the null controllability for parabolic SPDEs involving both the state and the gradient of the state. To start with, an improved global Carleman estimate for…