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

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.