  We study models of non-minimally coupled relativistic fluid and $k$-essence
scalar field in the background of a flat Friedmann-Lemaitre-Robertson-Walker
universe. The non-minimal coupling term is introduced in the Lagrangian level.
We employ the variational approach with respect to independent variables that
produce modified $k-$essence field equations and the Friedmann equations. We
have analyzed the coupled field-fluid framework explicitly using the dynamical
system technique considering two different models based on inverse power-law
potential. After examining these models it is seen that both models are capable
of producing accelerating attractor solutions satisfying adiabatic sound speed
conditions.
