English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

We consider the d-dimensional Boussinesq system defined on a sufficientlysmooth bounded domain, with homogeneous boundary conditions, and subject toexternal sources, assumed to cause instability. The initial conditions for bothfluid and heat equations are taken of low regularity. We then seek to uniformlystabilize such Boussinesq system in the vicinity of an unstable equilibriumpair, in the critical setting of correspondingly low regularity spaces, bymeans of explicitly constructed, feedback controls, which are localized on anarbitrarily small interior subdomain. In addition, they will be minimal innumber, and of reduced dimension: more precisely, they will be of dimension$(d-1)$ for the fluid component and of dimension $1$ for the heat component.The resulting space of well-posedness and stabilization is a suitable, tightBesov space for the fluid velocity component (close to $\mathbf{L}^3(\Omega$)for $ d = 3 $) and the space $L^q(\Omega$) for the thermal component, $ q > d$. Thus, this paper may be viewed as an extension of \cite{LPT.1}, where thesame interior localized uniform stabilization outcome was achieved by use offinite dimensional feedback controls for the Navier-Stokes equations, in thesame Besov setting.

discrete and continuous dynamical systems. series b

Uniform stabilization of Boussinesq systems in critical  $\mathbf{L}^q$-based Sobolev and Besov spaces by finite dimensional interior  localized feedback controls