Diffusion and mixing in fluid flow

By Peter Constantin, Alexander V. Kiselev, Lenya Ryzhik, Andrej Zlatoš. 2005

298 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering

View Paper: https://www.semanticscholar.org/paper/1caa609eb289daf9ce9b10d20992cb5f734ded6e

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Citations in the corpus

On the Euler equations of incompressible fluids (2007, methodology): “Strong rapid effects are studied using PDE methods ([17], [50], [55]).”
Enhanced Dissipation, Hypoellipticity, and Anomalous Small Noise Inviscid Limits in Shear Flows (2015, background): “This effect in linear equations has been studied previously in [6, 9, 15, 48, 50], in the physics literature [12, 19, 36, 40, 43], and in control theory [4, 5]; a closely related effect was also studied in [22].”
Inviscid damping and the asymptotic stability of planar shear flows in the 2D Euler equations (2013, background): “Also in both cases, the phenomena can be related to the continuous spectrum in the linear problem; for example, the RAGE theorem applies equally well to transport equations as to dispersive equations [26].”
Enhanced Dissipation and Inviscid Damping in the Inviscid Limit of the Navier–Stokes Equations Near the Two Dimensional Couette Flow (2014, methodology): “The work of [21] considers in a more general framework the connection between the spectral properties of the background flow and the enhanced dissipation effect in the context of passive tracers using the RAGE theorem (see also [11] for the elliptic case).”
Optimal stirring strategies for passive scalar mixing (2010, background): “…1997; D’Alessandro, Dahleh & Mezić 1999; Vikhansky 2002; Schumacher & Sreenivasan 2003; Balogh, Aamo & Krstic 2005; Mathew et al. 2005; Thiffeault & Finn 2006; Mathew et al. 2007; Constantin et al. 2008; Cortelezzi, Adrover & Giona 2008; Thiffeault & Pavliotis 2008; Gubanov & Cortelezzi 2010).”
Linear inviscid damping and enhanced dissipation for the Kolmogorov flow (2017, methodology): “See [3, 13, 20, 8, 9] and references therein for more relevant works.”
On the Loss of Continuity for Super-Critical Drift-Diffusion Equations (2012, background): “first eigenvalue estimates [3], mixing rates [11], and expected exit times [24].”
Enhanced dissipation and Hörmander's hypoellipticity (2021, background): “In [14], Constantin, Kiselev, Ryzhik, and Zlatoš investigated enhanced dissipation in broad generality in terms of spectral properties of the operator u ·∇.”
On the stability threshold for the 3D Couette flow in Sobolev regularity (2015, background): “4 for more discussion or previous works such as [45, 20, 34, 12, 4, 5, 17, 11, 6] ([20] are the first to the authors’ knowledge to observe that this is important for understanding (1.”