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physics.flu-dyn2024
Energy Method and Stability of Shear Flows: an Elementary Tutorial
Antonio Barletta, Giuseppe Mulone
This paper provides a pedagogical introduction to the classical nonlinear stability analysis of the plane Poiseuille and Couette flows. The whole procedure is kept as simple as pos…
physics.flu-dyn2023
Nonlinear monotone energy stability of plane shear flows: Joseph or Orr critical thresholds?
Giuseppe Mulone
Critical Reynolds numbers for the monotone exponential energy stability of Couette and Poiseuille plane flows were obtained by Orr 1907 \cite{Orr1907} in a famous paper, and by Jos…
physics.flu-dyn2018
Nonlinear stability results for plane Couette and Poiseuille flows
Paolo Falsaperla, Andrea Giacobbe, Giuseppe Mulone
In this article we prove, choosing an appropriately weighted -energy equivalent to the classical energy, that the plane Couette and Poiseuille flows are nonlinearly stable wit…