3 papers
math.AP2024
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_tρ=Δρ^m+ρg(ρ),\quad (x,t)\in \mathbb{R}^n\times \mathbb{R}_+,\quad n…
math.AP2024
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=Δn- \nabla \cdot…
math.AP2023
Incompressible limit of porous media equation with chemotaxis and growth
Qingyou He, Hai-Liang Li, Benoît Perthame
We revisit the problem of proving the incompressible limit for the compressible porous media equation with Newtonian drift and growth. The question is motivated by models of living…