Pré-Publication, Document De Travail Année : 2021

Spectral inequality for an Oseen operator in a two dimensional channel

Résumé

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.

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Dates et versions

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

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  • HAL Id : hal-03200711 , version 1

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