Global well-posedness of the three-dimensional viscous primitive equations with bounded delays

Abstract

<p style='text-indent:20px;'>The study of delay is one of the important problems in fluid mechanics. When we attempt to control the fluid in some sense, this delay may occur by applying a force that takes into account not only the current state of the system, but also the known history. In this paper, the three-dimensional viscous primitive equations with bounded delays are considered. We prove the existence of weak and strong solutions, and obtain the uniqueness of the strong solution. We also obtain the exponential decay behavior of the weak solutions and get some higher order estimates for strong solution. Under appropriate assumptions, we prove that the time-dependent weak solutions converge exponentially to the unique stationary solution.</p>