4 papers
Hele-Shaw limit of chemotaxis-Navier-Stokes flows
Qingyou He, Ling-Yun Shou, Leyun Wu
This paper investigates the connection between the chemotaxis--Navier--Stokes system with porous medium type nonlinear diffusion and the Hele--Shaw problem in ($d\ge…
Sharp power concavity of two relevant free boundary problems of reaction-diffusion type
Qingyou He
The porous medium type reaction-diffusion equation and the Hele-Shaw problem are two free boundary problems linked through the incompressible (Hele-Shaw) limit. We investigate and…
Porous medium type reaction-diffusion equation: large time behaviors and regularity of free boundary
Qingyou He
We consider the Cauchy problem of the porous medium type reaction-diffusion equation \begin{equation*} \partial_tÏ=ÎÏ^m+Ïg(Ï),\quad (x,t)\in \mathbb{R}^n\times \mathbb{R}_+,\q…
Global dynamics for the generalized chemotaxis-Navier-Stokes system in
Qingyou He, Ling-Yun Shou, Leyun Wu
We consider the chemotaxis-Navier-Stokes system with generalized fluid dissipation in : \begin{eqnarray*} \begin{cases} \partial_t n+u\cdot \nabla n=În- \nabla \cdot…