论文标题
用螺旋对称性的3D稳定Euler方程的降落化
Desingularization of 3D steady Euler equation with helical symmetry
论文作者
论文摘要
在本文中，我们研究了一般螺旋结构域中与螺旋对称性的3D不可压缩欧拉方程的稳定溶液的降低溶液。我们用螺旋对称性构建了一个稳定的欧拉流，因此相关的涡度渐近地趋于螺旋涡流丝。解决方案是通过用参数以发散形式求解半线性椭圆形问题获得的。通过使用流函数方法，我们显示了集中在单点附近的基态解决方案的存在和渐近行为，该点是参数$ \ varepsilon \至0 $。还讨论了这些解决方案的定性特性。
In this paper, we study desingularization of steady solutions of 3D incompressible Euler equation with helical symmetry in a general helical domain. We construct a family of steady Euler flows with helical symmetry, such that the associated vorticities tend asymptotically to a helical vortex filament. The solutions are obtained by solving a semilinear elliptic problem in divergence form with a parameter. By using the stream-function method, we show the existence and asymptotic behavior of ground state solutions concentrating near a single point as the parameter $ \varepsilon\to 0 $. Qualitative properties of those solutions are also discussed.
