  Dynamical low-rank approximation, as has been demonstrated recently, can be
extremely efficient in solving kinetic equations. However, a major deficiency
is that they do not preserve the structure of the underlying physical problem.
For example, the classic dynamical low-rank methods violate mass, momentum, and
energy conservation. In [L. Einkemmer, I. Joseph, J. Comput. Phys. 443:110495,
2021] a conservative dynamical low-rank approach has been proposed. However,
directly integrating the resulting equations of motion, similar to the classic
dynamical low-rank approach, results in an ill-posed scheme. In this work we
propose a robust, i.e. well-posed, integrator for the conservative dynamical
low-rank approach that conserves mass and momentum (up to machine precision)
and significantly improves energy conservation. We also report improved
qualitative results for some problems and show how the approach can be combined
with a rank adaptive scheme.
