  The primary challenge in solving kinetic equations, such as the Vlasov
equation, is the high-dimensional phase space. In this context, dynamical
low-rank approximations have emerged as a promising way to reduce the high
computational cost imposed by such problems. However, a major disadvantage of
this approach is that the physical structure of the underlying problem is not
preserved. In this paper, we propose a dynamical low-rank algorithm that
conserves mass, momentum, and energy as well as the corresponding continuity
equations. We also show how this approach can be combined with a conservative
time and space discretization.
