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In this paper, we will provide the the finite element method for the electro-osmotic flow in micro-channels, in which a convection-diffusion type equation is given for the charge density ρe. A time-di...
Rossby-Haurwitz waves are an important class of explicit solutions to the incompressible Euler equation on a rotating 2-sphere. We will introduce our recent work on the nonlinear stability of degree-2...
Stability conditions on triangulated categories are introduced by Bridgeland. For 3-Calabi-Yau triangulated categories from quivers with potentials, the space of stability conditions on this triangula...
We focus on numerical study of the dynamical Ginzburg-Landau equations under the temporal gauge, and propose a decoupled numerical scheme based on the finite element method. For the variable A, the se...
In this talk, we discuss the global stability of the Minkowski spacetime in the wave coordinates system for the massive Einstein-Vlasov system. In particular, compared with previous results by Lindbla...
We consider the existence, uniqueness and nonlinear stability of the travelling wave solution of the Navier-Stokes-Poisson system with density-dependent viscosity for ions. Firstly, we derive a system...
In his pioneering work in 1860, Riemann proposed the Riemann problem and solved it for isentropic gas in terms of shocks and rarefaction waves. It eventually became the foundation of the theory of one...
We will talk about our recent results on the convexity, uniqueness, and stability of regular reflection solutions for the potential flow equation in a natural class of self-similar solutions. The appr...
In this talk, I will discuss the stability conditions for a free boundary problem of compressible Euler equations coupled with a nonlinear Poisson equation of electric potential. Under those stability...
In this talk, we consider a class of exponential time differencing (ETD) schemes for solving the nonlocal Cahn-Hilliard equation. We first use the Fourier collocation method to discretize the space do...
Peaked soliton dynamics is one of the most intriguing features of the Camassa-Holm-type integrable equations. In this talk, I will give a review on the issue of the stability of peaked solitons, inclu...
Peaked soliton dynamics is one of the most intriguing features of the Camassa-Holm-type integrable equations. In this talk, I will give a review on the issue of the stability of peaked solitons, inclu...
In this talk, the combined quasi-neutral and zero-viscosity limits of the two-fluid Navier-Stokes-Poisson systems (one for ion and another for electron) with boundary are rigorously proved by investig...
As a key factor affecting the biogeochemical cycle of human existence, terrestrial vegetation is vulnerable to natural environment and human activities, with obvious temporal and spatial characteristi...
Hydrogels are polymer materials that can absorb a large amount of water, making them flexible like human tissue. They are used in a number of medical applications, including contact lenses, wound dres...

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