标题： 由对称性生成的三维纳维-斯托克斯方程中的涡旋和不变曲面 显示英文标题

标题： Vortices and invariants surfaces generated by symmetries for the 3D Navier-Stokes equations

摘要： 我们证明，不可压缩3D纳维-斯托克斯方程的李点对称性的某些无穷小算子会产生具有不同特征的涡旋解。 这种方法允许对涡旋进行代数分类，并揭示了涡量与涡旋拉伸矢量之间的对齐机制。 与纳维-斯托克斯方程相关的对称代数被证明是无限维的。 获得了新的涡旋结构，在某些情况下推广了已知的配置，例如，布赫纳和伦德格伦解，并根据动态角度的值进行了讨论。 还对在所研究方程的对称群下不变的边界条件进行了系统处理，并识别了相应的不变曲面。 显示英文摘要

摘要： We show that certain infinitesimal operators of the Lie-point symmetries of the incompressible 3D Navier-Stokes equations give rise to vortex solutions with different characteristics. This approach allows an algebraic classification of vortices and throws light on the alignment mechanism between the vorticity and the vortex stretching vector. The symmetry algebra associated with the Navier-Stokes equations turns out to be infinite- dimensional. New vortical structures, generalizing in some cases well-known configurations such as, for example, the Burgers and Lundgren solutions, are obtained and discussed in relation to the value of the dynamic angle. A systematic treatment of the boundary conditions invariant under the symmetry group of the equations under study is also performed, and the corresponding invariant surfaces are recognized.