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Academy of Mathematics and Systems Science, CAS Colloquia & Seminars：Stability conditions for a free boundary problem of 3-D compressible Euler equations coupled with a nonlinear Poisson equation
三维 可压缩欧拉方程 耦合 非线性泊松方程 自由边界问题 稳定性条件
2023/4/18
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...
The Harnack inequality for second-order elliptic equations with divergence-free drifts
Harnack inequality second-order elliptic equations divergence-free drifts
2015/7/14
We consider an elliptic equation with a divergence-free drift b. We prove that an inequality of Harnack type holds under the assumption b ∈ Ln/2+δ ∩ L2 where δ > 0. As an application we provide a one ...
Shock-free Solutions of the Compressible Euler Equations
Conservation laws compressible Euler equations singularity formation large data exact solutions
2012/4/18
We study the structure of shock-free solutions of the compressible Euler equations with large data. We describe conditions under which the Rarefactive/Compressive character of solutions changes, and c...
Regularity of solutions of a free boundary problem modeling the growth of solid tumors
Free boundary problem tumor model regularity
2011/10/15
In this paper we study a free boundary problem modeling the growth of solid tumors. Due to the free boundary and surface tension effects, this problem is a nonlinear problem involving non-local terms....
On the singular set of mean curvature flows with Neumann free boundary conditions
singular set of mean curvature flows Neumann free boundary conditions
2011/1/17
We consider n-dimensional hypersurfaces flowing by mean curvature flow with Neumann free
boundary conditions supported on a smooth support surface. We show that the Hausdorff n-measure of the singula...
Hyperbolic surface subgroups of one-ended doubles of free groups
hyperbolic group surface group diskbusting polygonality
2010/12/9
Gromov asked whether every one-ended word-hyperbolic group contains a hyperbolic surface group. We prove that every one-ended double of a free group contains a hyperbolic surface
group if the free gr...
Simple closed curves, word length, and nilpotent quotients of free groups
ISimple closed curves word length nilpotent quotients of free groups
2010/11/29
We consider the fundamental group p of a surface of finite type equipped with the infinite generating set consisting of all simple closed curves. We show that every nilpotent quotient of p has finite ...