  The 3D primitive equations are used in most geophysical fluid models to
approximate the large scale oceanic and atmospheric dynamics. We prove that
there do not exist smooth stationary solutions to the 3D primitive equations
with compact support, independently of the presence of the Coriolis rotation
term or the viscosity. This result is in strong contrast with the recently
established existence of compactly supported smooth solutions to the
incompressible 3D Euler equations.
