Volume 7 (2024)
Mecherbet, Amina;  Sueur, Franck
A few remarks on the transport-Stokes system
Annales Henri Lebesgue, Volume 7 (2024), pp. 1367-1408.

Metadata

DOI10.5802/ahl.222
Keywords Stokes flow, transport equation, Suspensions, global existence and uniqueness results for PDEs, Analyticity, controllability

Abstract

We consider the so-called transport-Stokes system which describes sedimentation of inertialess suspensions in a viscous flow and couples a transport equation and the steady Stokes equations in the full three-dimensional space. First we present a global existence and uniqueness result for L 1 ∩L p initial densities where p≥3. Secondly, we prove that, in the case where p>3, the flow map which describes the trajectories of these solutions is analytic with respect to time. Finally we establish the small-time global exact controllability of the transport-Stokes system. These results extend to the transport-Stokes system some results obtained for the incompressible Euler system respectively by Yudovich in [Yud63], by Chemin in [Che92, Che95] and by Coron, and Glass, in [Cor96, Gla00].


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