  Recently, Huang and Qin \cite{HY01} introduced the Gaussian chord measure and
$L_p$-Gaussian chord measure by variational methods. Meanwhile, they posed
Gaussian chord Minkowski problem for $p=1$ and used variational methods to
obtain an origin-symmetric normalized measure solution for the Gaussian chord
Minkowski problem. The smooth solution, up to now, to the $L_p$-Gaussian chord
Minkowski problem is still open.
  Motivated by the forgoing works by Huang and Qin in \cite{HY01}, we propose
in the present paper the $L_p(p>0)$-Gaussian chord Minkowski problem and
log-Gaussian chord Minkowski problem, and obtain the smooth even solutions to
these two types of problems by the method of a Gauss curvature flow.
