论文标题
关于固定Navier-Stokes方程的自相似解决方案的分叉
On bifurcation of self-similar solutions of the stationary Navier-Stokes equations
论文作者
论文摘要
Landau解决方案是在三维空间中固定不可压缩的Navier-Stokes方程的特殊解决方案。它们是自相似的，轴对称，没有漩涡。实际上，任何自相似平滑的解决方案都必须是Landau解决方案。为了将此结果扩展到解决方案类别的一个，具有点刻度的尺度限制$ | u（x）| \ leq c_0 | x | x |^{ - 1} $对于某些$ c_0> 0 $，我们考虑axissymmmetric ovely siby sim-simelliar simerilar solutions，并研究了从某些Landau解决方案中散发出的解决方案的存在。我们证明，漩涡成分的包含不会增强分叉，并提供了无分叉的数值证据。
Landau solutions are special solutions to the stationary incompressible Navier-Stokes equations in the three dimensional space excluding the origin. They are self-similar and axisymmetric with no swirl. In fact, any self-similar smooth solution must be a Landau solution. In the effort of extending this result to the one for the solution class with the pointwise scale-invariant bound $|u(x)|\leq C_0|x|^{-1}$ for some $C_0>0$, we consider axisymmetric discretely self-similar solutions, and investigate the existence of such solution curve emanating from some Landau solution. We prove that the inclusion of the swirl component does not enhance the bifurcation and present numerical evidence of no bifurcation.
