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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.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…
math.AP2024
Convergence of Free Boundaries in the Incompressible Limit of Tumor Growth Models
Jiajun Tong, Yuming Paul Zhang
We investigate the general Porous Medium Equations with drift and source terms that model tumor growth. Incompressible limit of such models has been well-studied in the literature,…