Abstract
We study the large time behavior of solutions to two-dimensional Euler and Navier-Stokes equations linearized about shear flows of the mixing layer type in the unbounded channel T×R. Under a simple spectral stability assumption on a self-adjoint operator, we prove a local form of the linear inviscid damping that is uniform with respect to small viscosity. We also prove a local form of the enhanced viscous dissipation that takes place at times of order ν−1/3, ν being the small viscosity. To prove these results, we use a Hamiltonian approach, following the conjugate operator method developed in the study of Schrödinger operators, combined with a hypocoercivity argument to handle the viscous case.
| Original language | English (US) |
|---|---|
| Article number | 108339 |
| Journal | Journal of Functional Analysis |
| Volume | 278 |
| Issue number | 3 |
| DOIs | |
| State | Accepted/In press - Jan 1 2019 |
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All Science Journal Classification (ASJC) codes
- Analysis
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Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method. / Grenier, Emmanuel; Nguyen, Toan T.; Rousset, Frédéric; Soffer, Avy.
In: Journal of Functional Analysis, Vol. 278, No. 3, 108339, 01.02.2020.Research output: Contribution to journal › Article
TY - JOUR
T1 - Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method
AU - Grenier, Emmanuel
AU - Nguyen, Toan T.
AU - Rousset, Frédéric
AU - Soffer, Avy
PY - 2019/1/1
Y1 - 2019/1/1
N2 - We study the large time behavior of solutions to two-dimensional Euler and Navier-Stokes equations linearized about shear flows of the mixing layer type in the unbounded channel T×R. Under a simple spectral stability assumption on a self-adjoint operator, we prove a local form of the linear inviscid damping that is uniform with respect to small viscosity. We also prove a local form of the enhanced viscous dissipation that takes place at times of order ν−1/3, ν being the small viscosity. To prove these results, we use a Hamiltonian approach, following the conjugate operator method developed in the study of Schrödinger operators, combined with a hypocoercivity argument to handle the viscous case.
AB - We study the large time behavior of solutions to two-dimensional Euler and Navier-Stokes equations linearized about shear flows of the mixing layer type in the unbounded channel T×R. Under a simple spectral stability assumption on a self-adjoint operator, we prove a local form of the linear inviscid damping that is uniform with respect to small viscosity. We also prove a local form of the enhanced viscous dissipation that takes place at times of order ν−1/3, ν being the small viscosity. To prove these results, we use a Hamiltonian approach, following the conjugate operator method developed in the study of Schrödinger operators, combined with a hypocoercivity argument to handle the viscous case.
UR - http://www.scopus.com/inward/record.url?scp=85073572574&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85073572574&partnerID=8YFLogxK
U2 - 10.1016/j.jfa.2019.108339
DO - 10.1016/j.jfa.2019.108339
M3 - Article
AN - SCOPUS:85073572574
VL - 278
JO - Journal of Functional Analysis
JF - Journal of Functional Analysis
SN - 0022-1236
IS - 3
M1 - 108339
ER -