38 citations · 64 across the 7 of their papers we have counts for
7 papers
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…
Monotone energy stability for Poiseuille flow in a porous medium
Giuseppe Mulone
We study the monotone energy stability of ``Poiseuille flow" in a plane-parallel channel with a saturated porous medium modeled by the Brinkman equation, on the basis of an analogy…
Squire's theorem for nonlinear monotone energy stability
Giuseppe Mulone
The Squire's theorem holds for parallel shear flows governed by the linearized Navier-Stokes equations. Squire writes ``For the study of the stability of flow between parallel wall…
Monotone energy stability of magnetohydrodynamics Couette and Hartmann flows
Giuseppe Mulone
We study the monotone nonlinear energy stability of \textit{magnetohydrodynamics plane shear flows, Couette and Hartmann flows}. We prove that the least stabilizing perturbations,…
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…
Energy stability of plane Couette and Poiseuille flows and Couette paradox
Paolo Falsaperla, Giuseppe Mulone, Carla Perrone
We study the nonlinear stability of plane Couette and Poiseuille flows with the Lyapunov second method by using the classical L2-energy. We prove that the streamwise perturbations…
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…