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) |
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Article number | 108339 |
Journal | Journal of Functional Analysis |
Volume | 278 |
Issue number | 3 |
DOIs | |
State | Published - Feb 1 2020 |
All Science Journal Classification (ASJC) codes
- Analysis