A simple proof of the Cucker-Smale flocking dynamics and mean-field limit
- Seung‐Yeal Ha, Jian‐Guo Liu
- Mathematics
- 1 June 2009
We present a simple proof on the formation of flocking to the Cucker-Smale system based on the explicit construction of a Lyapunov functional. Our results also provide a unified condition on the…
Thin film epitaxy with or without slope selection
- Bo Li, Jian‐Guo Liu
- PhysicsEuropean journal of applied mathematics
- 1 December 2003
Two nonlinear diffusion equations for thin film epitaxy, with or without slope selection, are studied in this work. The nonlinearity models the Ehrlich–Schwoebel effect – the kinetic asymmetry in…
A coupled chemotaxis-fluid model: Global existence
- Jian‐Guo Liu, A. Lorz
- Mathematics
- 1 September 2011
Kinetic formulation and global existence for the Hall-Magneto-hydrodynamics system
- Marion Arichetogaray, P. Degond, A. Frouvelle, Jian‐Guo Liu
- Physics, Mathematics
- 18 August 2011
This paper deals with the derivation and analysis of the the Hall Magneto-Hydrodynamic equations. We first provide a derivation of this system from a two-fluids Euler-Maxwell system for electrons and…
Well-posedness for Hall-magnetohydrodynamics
- D. Chae, P. Degond, Jian‐Guo Liu
- Mathematics
- 17 December 2012
Accurate, stable and efficient Navier-Stokes solvers based on explicit treatment of the pressure term
- Hans Johnston, Jian‐Guo Liu
- Computer Science
- 1 September 2004
Projection method I: convergence and numerical boundary layers
- E. Weinan, Jian‐Guo Liu
- Engineering
- 1 August 1995
This is the first of a series of papers on the subject of projection methods for viscous incompressible flow calculations. The purpose of these papers is to provide a thorough understanding of the ...
Vorticity Boundary Condition and Related Issues for Finite Difference Schemes
- E. Weinan, Jian‐Guo Liu
- Mathematics
- 15 March 1996
This paper discusses three basic issues related to the design of finite difference schemes forunsteadyviscous incompressible flows using vorticity formulations: the boundary condition for vorticity,…
A High-Order Discontinuous Galerkin Method for 2D Incompressible Flows
- Jian‐Guo Liu, Chi-Wang Shu
- Computer Science
- 20 May 2000
A high-order discontinuous Galerkin method for two-dimensional incompressible flow in the vorticity stream-function formulation, which is efficient for inviscid or high Reynolds number flows.
On the diffusion approximation of nonconvex stochastic gradient descent
- Wenqing Hu, C. J. Li, Lei Li, Jian‐Guo Liu
- Computer ScienceAnnals of Mathematical Sciences and Applications
- 22 May 2017
It is proved rigorously that the diffusion process can approximate the SGD algorithm weakly using the weak form of master equation for probability evolution, and the effects of batch size for the deep neural networks are discussed, finding that small batch size is helpful for SGD algorithms to escape unstable stationary points and sharp minimizers.
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