论文标题
奇异域上2D Euler方程的正涡度解决方案的唯一性
Uniqueness of Positive Vorticity Solutions to the 2D Euler Equations on Singular Domains
论文作者
论文摘要
我们表明，在相当限制的简单连接域上，针对2D Euler方程的正涡度解的粒子轨迹无法在有限的时间内到达边界。这包括可能无处$ c^1 $边界的域，并具有任意角度的角落，并且当域具有较大的角度角时，可能会失败而没有符号假设。因此，此类域上的正涡度解决方案是Lagrangian，如果涡度最初是在边界附近恒定的，我们也会获得它们的独特性。
We show that particle trajectories for positive vorticity solutions to the 2D Euler equations on fairly general bounded simply connected domains cannot reach the boundary in finite time. This includes domains with possibly nowhere $C^1$ boundaries and having corners with arbitrary angles, and can fail without the sign hypothesis when the domain has large angle corners. Hence positive vorticity solutions on such domains are Lagrangian, and we also obtain their uniqueness if the vorticity is initially constant near the boundary.
