A stability result for the identification of a permeability parameter on Navier–Stokes equations

Abstract In this work, we present a stability result for the inverse problem of recovering smooth scalar permeability parameter given by Brinkman’s law applied to steady Navier–Stokes equations from local observations fluid velocity on fixed domain. comparison with (Choulli et al 2013 Appl. Anal. 92 2127–43), prove logarithmic estimate under weaker assumptions, since our proof is based in strategy that does not require pressure observations. This kind or are useful problems soft tissue elastography (see Honarvar 2012 Phys. Med. Biol. 57 5909–27). Finally, some numerical tests validate theoretical results.