Linear inviscid damping and enhanced viscous dissipation of shear flows by using the conjugate operator method

Emmanuel Grenier, Toan T. Nguyen, Frédéric Rousset, Avy Soffer

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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 languageEnglish (US)
Article number108339
JournalJournal of Functional Analysis
Issue number3
StatePublished - Feb 1 2020


All Science Journal Classification (ASJC) codes

  • Analysis

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