Robustness of regularity for the 3D convective Brinkman–Forchheimer equations

Abstract

We prove a robustness of regularity result for the 3D convective Brinkman–Forchheimer equations∂tu−μΔu+(u⋅∇)u+∇p+αu+β|u|r−1u=f, for the range of the absorption exponent r∈[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 3D incompressible Navier–Stokes equations by Chernyshenko et al. [5] and Dashti & Robinson [8].