4 papers
Superlinear gradient growth for 2D Euler equation without boundary
In-Jee Jeong, Yao Yao, Tao Zhou
We consider the vorticity gradient growth of solutions to the two-dimensional Euler equations in domains without boundary, namely in the torus and the whole plane…
Finite time blowup for Keller-Segel equation with logistic damping in three dimensions
Jiaqi Liu, Yixuan Wang, Tao Zhou
The Keller-Segel equation, a classical chemotaxis model, and many of its variants have been extensively studied for decades. In this work, we focus on 3D Keller-Segel equation with…
Nonradial stability of self-similar blowup to Keller-Segel equation in three dimensions
Zexing Li, Tao Zhou
In three dimensions, the parabolic-elliptic Keller-Segel system exhibits a rich variety of singularity formations. Notably, it admits an explicit self-similar blow-up solution whos…
Finite-time blowup for Keller-Segel-Navier-Stokes system in three dimensions
Zexing Li, Tao Zhou
While finite-time blowup solutions have been studied in depth for the Keller-Segel equation, a fundamental model describing chemotaxis, the existence of finite-time blowup solution…