Regular and Singular Steady States of the 2D Incompressible Euler Equations near the Bahouri–Chemin Patch

We consider steady states of the two-dimensional incompressible Euler equations on \({\mathbb {T}}^2\) and construct smooth and singular steady states around a particular singular steady state. More precisely, we construct families of smooth and singular steady solutions that converge to the Bahouri–Chemin patch.