论文标题
具有小横截面的螺旋涡旋，用于3D不可压缩的Euler方程
Helical vortices with small cross-section for 3D incompressible Euler equation
论文作者
论文摘要
在本文中，我们在无限管道中构建了带有小横截面的行进旋转螺旋涡旋，与3D不可压缩的Euler方程构造，该管道趋于渐近地趋向于通过二线曲率流而演变而来的奇异螺旋涡流丝。该构建基于研究差异形式\ begin {equation*} \ begin {cases} - \ varepsilon^2 \ text {div}（k（x）\ nabla u）=（u -q | \ ln \ ln \ varepsilon |） u = 0，\ \＆x \ in \partialΩ，\ end {cases} \ end {equation*}对于$ \ varepsilon的小值。还构建了$螺旋涡流溶液，这些溶液集中在几个带有多边形对称性的螺旋丝附近。
In this article, we construct traveling-rotating helical vortices with small cross-section to the 3D incompressible Euler equations in an infinite pipe, which tend asymptotically to singular helical vortex filament evolved by the binormal curvature flow. The construction is based on studying a general semilinear elliptic problem in divergence form \begin{equation*} \begin{cases} -\varepsilon^2\text{div}(K(x)\nabla u)= (u-q|\ln\varepsilon|)^{p}_+,\ \ &x\in Ω,\\ u=0,\ \ &x\in\partial Ω, \end{cases} \end{equation*} for small values of $ \varepsilon. $ Helical vortex solutions concentrating near several helical filaments with polygonal symmetry are also constructed.
