  In this paper, we study the approximate controllability of a system governed
by an evolution problem known as the sloshing problem. This problem involves a
spatial, nonlocal differential operator inherent in the dynamics of a
two-dimensional, incompressible, non-viscous fluid within a confined domain.
Our work establishes unique continuation results that enable the application of
source control localized in an interior domain, allowing the aforementioned
controllability.
