Linear Inviscid Damping and Enhanced Viscous Dissipation Via Dispersive Estimates

Linear Inviscid Damping and Enhanced Viscous Dissipation Via Dispersive Estimates

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Avraham Soffer, Rutgers
Fine Hall 322

We study the large time behavior of solutions to two-dimensional Euler and Navier-Stokes equations linearized about shearflows 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 Schroedinger operators, combined with a hypocoercivity argument to handle the viscous case.