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