论文标题
Euler和Lake方程的涡流运动
Vortex motion of the Euler and Lake equations
论文作者
论文摘要
我们首先调查整个平面，半平面和象限的Euler方程的平面点涡流运动。然后，我们继续使用半平面中的2涡流系统的轨道的明确形式来证明2涡流系统的非碰撞属性。我们还证明，半平面中的$ n $ - 伏特还无法以$ n> 2 $整合，这是由数值实验提出的，没有严格的证明。 $ \ Mathbb r^n，\; n \ geq3 $带有某些对称性的Skew-mean-curvator（或二维）流，可被视为2D湖方程的点涡流运动。我们比较了Euler和Lake方程的点涡流运动。解决了半平面，象限和同轴涡流环的双剂运动，球体乘积膜之间的有趣相似之处。我们还在论文中提出了一些公开问题。
We start by surveying the planar point vortex motion of the Euler equations in the whole plane, half-plane and quadrant. Then we go on to prove non-collision property of 2-vortex system by using the explicit form of orbits of 2-vortex system in the half-plane. We also prove that the $N$-vortex system in the half-plane is nonintegrable for $N>2$, which is suggested previously by numerical experiments without rigorous proof. The skew-mean-curvature (or binormal) flow in $\mathbb R^n,\;n\geq3$ with certain symmetry can be regarded as point vortex motion of the 2D lake equations. We compare point vortex motions of the Euler and lake equations. Interesting similarities between the point vortex motion in the half-plane, quadrant and the binormal motion of coaxial vortex rings, sphere product membranes are addressed. We also raise some open questions in the paper.
