Dynamics of purely kinetic $k$-essence in presence of a perfect fluid
  We investigate the dynamics of purely kinetic $k$-essence scalar field in
three different scenarios. We begin with the case of a purely kinetic
$k$-essence theory and try to formulate a late time accelerating universe
model. Then we introduce a perfect fluid in presence of the purely kinetic
$k$-essence field and calculate how the features of the previous model are
modified. We discuss two cases primarily, in the first case the fluid and the
scalar field does not exchange energy and momentum and in the later case the
scalar field and the fluid interact non-minimally and exchange energy and
momentum. Using dynamical analysis technique, we examine the stability of these
systems in the background of a spatially flat
Friedman-Lemaitre-Robertson-Walker (FLRW) universe for a particular chosen
functional form of $k$-essence kinetic energy term. From the evolution of the
effective equation of state parameter of the field-fluid system we conclude
that a non-minimally coupled field-fluid scenario can produce physically
interesting results. We also find that the $k$-essence field can effectively
hide in a radiation background.
