3 papers
math.AP2026
Uniformly Rotating Vortex Patches with 90-Degree Corners
De Huang, Jiajun Tong, Xiaopeng Zheng
For the 2-D incompressible Euler equation, we prove the existence of -fold symmetric uniformly rotating vortex patches with 90-degree corners for all . Properties of t…
math.AP2026
Novel Self-similar Finite-time Blowups with Singular Profiles of the 1D Hou-Luo Model and the 2D Boussinesq Equations: A Numerical Investigation
Bojin Chen, De Huang, Xiangyuan Li
We present novel self-similar finite-time blowup scenarios for the 1D Hou--Luo model. We numerically demonstrate that solutions that initially satisfy certain derivative degeneracy…
math.AP2024
Steady Contiguous Vortex-Patch Dipole Solutions of the 2D Incompressible Euler Equation
De Huang, Jiajun Tong
We rigorously construct the first steady traveling wave solutions of the 2D incompressible Euler equation that take the form of a contiguous vortex-patch dipole, which can be viewe…