Large-time behavior of solutions to the inflow problem of the
non-isentropic micropolar fluid model
Abstract
We investigate the asymptotic behavior of solutions to the initial
boundary value problem for the micropolar fluid model in a half line
$\R_{+}:=(0,\infty).$ Inspired by the
relationship between micropolar fluid and Navier-Stokes, we prove that
the composite wave onsisting of the transonic boundary layer solution,
the 1-rarefaction wave, the viscous 2-contact wave and the 3-rarefaction
wave for the inflow problem on the micropolar fluid model is
time-asymptotically stable under some smallness conditions. Meanwhile,
we obtain the global existence of solutions based on the basic energy
method.