5 papers
Global well-posedness and scattering for defocusing energy-critical inhomogeneous NLS in dimensions
Bo Yang, Lei Zhang, Bin Liu
We study the defocusing energy-critical inhomogeneous nonlinear Schrödinger equation \[ i\partial_tu+Îu=|x|^{-b}|u|^{\frac{4-2b}{d-2}}u, \qquad (t,x)\in\R\times\R^d, \] with init…
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…
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…
New results on the global solvability and blow-up for a class of weakly dissipative Camassa-Holm equations
Lei Zhang, Bin Liu
In this paper, we consider the Cauchy problem for a class of weakly dissipative Camassa-Holm equations in nonhomogeneous Besov spaces. First, we prove that the Cauchy problem admit…