In this talk, we will start by surveying the planar point vortex motion of the Euler equations in the whole plane, half-plane and quadrant. Then we are going to show a non-collision property of a 2-vortex system in the half-plane. We will also prove that the $N$-vortex system in the half-plane is nonintegrable for $N>2$, which was suggested previously by numerical experiments without a rigorous proof.
The skew-mean-curvature (or binormal) flow in $R^n$, $n>2$ with certain symmetry can be regarded as point vortex motion of the 2D lake equations. We will compare point vortex motions of the Euler and lake equations. Interesting similarities will be addressed. Finally, we will raise some open questions.
The talk will be via Zoom at:
https://utoronto.zoom.us/j/99576627828
Passcode: 448487