Imperial College London
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DrMicheleCoti Zelati

Faculty of Natural Sciences, Department of Mathematics

Royal Society University Research Fellow
 
 
 
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6M33Huxley BuildingSouth Kensington Campus

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Summary

 

Publications

Citation

BibTex format

@article{Coti:2023:10.1007/s00205-023-01842-3,
author = {Coti, Zelati M and Elgindi, TM and Widmayer, K},
doi = {10.1007/s00205-023-01842-3},
journal = {Archive for Rational Mechanics and Analysis},
title = {Stationary Structures Near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations},
url = {http://dx.doi.org/10.1007/s00205-023-01842-3},
volume = {247},
year = {2023}
}
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RIS format (EndNote, RefMan)

TY  - JOUR
AB  - <jats:title>Abstract</jats:title><jats:p>We study the behavior of solutions to the incompressible 2<jats:italic>d</jats:italic> Euler equations near two canonical shear flows with critical points, the Kolmogorov and Poiseuille flows, with consequences for the associated Navier–Stokes problems. We exhibit a large family of new, non-trivial stationary states that are arbitrarily close to the Kolmogorov flow on the square torus <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathbb {T}^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">                  <mml:msup>                    <mml:mrow>                      <mml:mi>T</mml:mi>                    </mml:mrow>                    <mml:mn>2</mml:mn>                  </mml:msup>                </mml:math></jats:alternatives></jats:inline-formula> in analytic regularity. This situation contrasts strongly with the setting of some monotone shear flows, such as the Couette flow: there the linearized problem exhibits an “inviscid damping” mechanism that leads to relaxation of perturbations of the base flows back to nearby shear flows. Our results show that such a simple description of the long-time behavior is not possible for solutions near the Kolmogorov flow on <jats:inline-formula><jats:alternatives><jats:tex-math>$$\mathbb {T}^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML">                  <mml:msup>                    <mml:mrow>                      <mml:mi>T</mml:mi>                    </mml:mrow>                    <mml:mn>2</mml:mn>                  </mml:msup>                </mml:math></jats:alternatives></jats:inline-formula>. Our construction of the new stationary states builds on a degenerac
AU  - Coti,Zelati M
AU  - Elgindi,TM
AU  - Widmayer,K
DO  - 10.1007/s00205-023-01842-3
PY  - 2023///
SN  - 0003-9527
TI  - Stationary Structures Near the Kolmogorov and Poiseuille Flows in the 2d Euler Equations
T2  - Archive for Rational Mechanics and Analysis
UR  - http://dx.doi.org/10.1007/s00205-023-01842-3
VL  - 247
ER  -
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