Spectral inequality for an Oseen operator in a two dimensional channel - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Preprints, Working Papers, ... Year : 2021

Spectral inequality for an Oseen operator in a two dimensional channel

Abstract

We prove a Lebeau-Robbiano spectral inequality for the Oseen operator in a two dimensional channel, that is, the linearized Navier-Stokes operator around a laminar flow, with no-slip boundary conditions. The operator being non-self-adjoint, we place ourself into the abstract setting of [12], and prove the spectral inequaltiy through the derivation of a proper Carleman estimate. In the spirit of [4], we handle the vorticity near the boundary by using the characteristics sets of $P_ϕ$ or $Q_{ϕ0}$ in the different microlocal regions of the cotangent space. As a consequence of the spectral inequality, we derive a new estimate of the cost of the control for the small-time null-controllability.
Fichier principal
Vignette du fichier
BuffeGagnon-Oseenequation.pdf (479.92 Ko) Télécharger le fichier
Origin : Files produced by the author(s)

Dates and versions

hal-03200711 , version 1 (16-04-2021)

Identifiers

  • HAL Id : hal-03200711 , version 1

Cite

Rémi Buffe, Ludovick Gagnon. Spectral inequality for an Oseen operator in a two dimensional channel. 2021. ⟨hal-03200711⟩
124 View
78 Download

Share

Gmail Facebook X LinkedIn More