Analysis of Fluids and Related Topics: Linear Inviscid Damping and Enhanced Viscous Dissipation Via Dispersive Estimates, Avraham Soffer, Rutgers University

Analysis of Fluids and Related Topics
  • Avraham Soffer
  • Rutgers University
  • Linear Inviscid Damping and Enhanced Viscous Dissipation Via Dispersive Estimates
Oct 18, 2018
4:30 pm
Fine Hall 322

Speaker: Avraham Soffer, Rutgers University

Abstract: 

We study the large time behavior of solutions to two-dimensional Eulerand 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 orderν^(−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.