Strong solutions to the equations of the unconsolidated porous media in 3D thin domains

Abstract

We prove the existence of global in time strong solutions of incompressible flow equations through isotropic granular (unconsolidated) porous media in thin domains of the form ${\mathrm{\Omega }}_{ϵ}:={\mathbb{R}}^2\times (0,ϵ)$ with $ϵ\in (0,1]$. Also, we demonstrate that as $ϵ\to 0^{+}$ the fluid velocity tends to vanish away from the initial time.

KEYWORDS:

• Porous medium
• thin domain
• Navier–Stokes equations

AMS CLASSIFICATIONS:

• 35Q35
• 76D03
• 76S99

Acknowledgments

The authors also express their gratitude to the anonymous referee for his/her various suggestions that improved the presentation of this manuscript.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

Marko A. Rojas-Medar was partially supported by MATH-AmSud project 21-MATH-03 (CTMicrAAPDEs), CAPES-PRINT #88881.311964/2018–01 (Brazil) and Project UTA-Mayor 4753-20, Universidad de Tarapacá, Arica-Chile and Felipe W. Cruz was partially supported by CNPq (Brazil).