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 - 2020/2/1
Y1 - 2020/2/1
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.
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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 -