  We consider the spatially inhomogeneous Landau equation with Maxwellian and
hard potentials (i.e with $\gamma\in[0,1)$) on the whole space $\mathbb{R}^3$.
We prove that if the initial data $f_{\text{in}}$ are close to the vacuum
solution $f_{\text{vac}}=0$ in an appropriate weighted norm then the solution
$f$ exists globally in time. This work builds up on the author's earlier work
on local existence of solutions to Landau equation with hard potentials. Our
proof uses $L^2$ estimates and exploits the null-structure established by Luk
[Stability of vacuum for the Landau equation with moderately soft potentials,
Annals of PDE (2019) 5:11]. To be able to close our estimates, we have to
couple the weighted energy estimates, which were established by the author in a
previous paper [Local existence for the Landau equation with hard potentials,
arXiv:1910.11866], with the null-structure and devise new weighted norms that
take this into account.
