  Observations and numerical simulations of laboratory and space plasmas in
almost collisionless regimes reveal anisotropic and non-gyrotropic particle
distribution functions. We investigate how such states can persist in the
presence of a sheared flow. We focus our attention on the pressure tensor
equation in a magnetized plasma and derive analytical self-consistent plasma
equilibria which exhibit a novel asymmetry with respect to the magnetic field
direction. These results are relevant for investigating, within fluid models
that retain the full pressure tensor dynamics, plasma configurations where a
background shear flow is present.
