Robustness of Regularity for the $3$D Convective Brinkman-Forchheimer Equations

Abstract

We prove a robustness of regularity result for the $3$D convective Brinkman-Forchheimer equations $$ \partial_tu -μΔu + (u \cdot \nabla)u + \nabla p + αu + β\abs{u}^{r - 1}u = f, $$ for the range of the absorption exponent $r\in [1,3]$ (for $r>3$ there exist global-in-time regular solutions), i.e. we show that strong solutions of these equations remain strong under small enough changes of the initial condition and forcing function. We provide a smallness condition which is similar to the robustness conditions given for the $3$D incompressible Navier-Stokes equations by Chernyshenko et al. (2007) and Dashti & Robinson (2008).

22 pages