Enhanced Dissipation and Transition Threshold for the Poiseuille Flow in a Periodic Strip
Augusto Del Zotto
Source abstract
Abstract. We consider the solution to the two-dimensional Navier–Stokes equations around the Poiseuille flow [Formula: see text] on [Formula: see text] with small viscosity [Formula: see text]. Via a hypocoercivity argument, we prove that the [Formula: see text]-dependent modes of the solution to the linear problem undergo the enhanced dissipation effect with a rate proportional to [Formula: see text]. Moreover, we study the nonlinear enhanced dissipation effect and we establish a transition threshold of [Formula: see text] for initial data in [Formula: see text]. Namely, when the [Formula: see text] norm of the perturbation of the Poiseuille flow is size at most [Formula: see text], its size remains so for all times and the enhanced dissipation persists with a rate proportional to [Formula: see text].
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