A remark on the stability problem in fluid dynamics
We show how one of the mentioned \textit{V. I. Arnold}'s results [e.g.: Mathematical methods of classical mechanics (1978; Zbl 0386.70001)] can be extended to some limit cases which are nontrivial from a physical point of view. The result will be obtained by constructing a one- parameter family of auxiliary functions which assures the stability of the stationary flow. Arnold's procedure has been used in more general problems of the physics of fluids and plasmas. We think that, also in these problems, the approach proposed here could be useful. Finally, we remark that other methods have been used to study the stability problem for fluids and plasmas getting results which have some overlap with the present one.
one-parameter family of auxiliary functions
scientific article; zbMATH DE number 4018637
scientific article