In most fluid dynamics problems, the governing equations are nonlinear because of the presence of convective terms. Nevertheless, existence of solutions can be shown by direct sum provided one identifies, in the relevant Banach space of solutions, particular subspaces which are invariant under time evolution. As an example, we consider classical convection problems and show how symmetry arguments can help in identifying such subspaces, as well as the role it can play in some stability issues.

中文翻译：

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关于对流中的对称性的注意事项

在大多数流体动力学问题中，由于存在对流项，因此控制方程是非线性的。但是，只要在相关的Banach空间中确定在时间演化下不变的特定子空间，就可以用直接和来表示解的存在。例如，我们考虑经典对流问题，并展示对称参数如何帮助识别此类子空间，以及对称性在某些稳定性问题中可以发挥的作用。