论文标题
在凸面平面域中的Euler方程的稳定解决方案上
On stable solutions to the Euler equations in convex planar domains
论文作者
论文摘要
在凸面平面域中，如果具有一个符号的初始涡度，我们研究了初始涡度的coadchoint轨道中动态稳定溶液的规则性和几何特性。这些流有椭圆停滞点。在数据上的某些非修饰条件下，我们表明它们是持有人连续的，并且具有凸水平曲线。我们还为停滞点提供了详细的描述。如果初始涡度具有良好的水平拓扑结构，则这些稳定的溶液位于coadhexhexhinexhinexhight Orbit的l^\ Infty-Strong闭合中。我们还展示了我们做出的大多数假设的清晰度。
In convex planar domains, given an initial vorticity with one sign, we study the regularity and geometric properties of the dynamically stable solutions to the Euler equations in the coadjoint orbit of the initial vorticity. These flows have elliptic stagnation points. Under some nondegeneracy conditions on the data, we show they are Holder continuous and have convex level curves. We also give a detailed description for the set of stagnation points. If the initial vorticity has nice level set topology, these stable solutions are in the L^\infty-strong closure of the coadjoint orbit. We also demonstrate the sharpness of most assumptions we made.
