  We study a regularized version of the Landau equation, which was recently
introduced in~\cite{CHWW20} to numerically approximate the Landau equation with
good accuracy at reasonable computational cost. We develop the existence and
uniqueness theory for weak solutions, and we reinforce the numerical findings
in~\cite{CHWW20} by rigorously proving the validity of particle approximations
to the regularized Landau equation.
