Abstract: This talk focuses on the recent progress on nonlinear structural stability of Hagen-Poiseuille flows in a pipe, in particular, the uniform stability of these flows with respect to the mass flux. The key ingredient of the analysis is the linear structural stability of Hagen-Poiseuille flows in a pipe. This linear problem closely relates to dynamical stability of Hagen-Poiseuille flows. The existence of a class of large solutions in a pipe will also be addressed even when the external force is large.

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