  The M dwarf star GJ 436 hosts a warm-Neptune that is losing substantial
amount of atmosphere, which is then shaped by the interactions with the wind of
the host star. The stellar wind is formed by particles and magnetic fields that
shape the exo-space weather around the exoplanet GJ 436 b. Here, we use the
recently published magnetic map of GJ 436 to model its 3D Alfv\'en-wave driven
wind. By comparing our results with previous transmission spectroscopic models
and measurements of non-thermal velocities at the transition region of GJ 436,
our models indicate that the wind of GJ 436 is powered by a smaller flux of
Alfv\'en waves than that powering the wind of the Sun. This suggests that the
canonical flux of Alfv\'en waves assumed in solar wind models might not be
applicable to the winds of old M dwarf stars. Compared to the solar wind, GJ
436's wind has a weaker acceleration and an extended sub-Alfv\'enic region.
This is important because it places the orbit of GJ 436 b inside the region
dominated by the stellar magnetic field (i.e., inside the Alfv\'en surface).
Due to the sub-Alfv\'enic motion of the planet through the stellar wind,
magnetohydrodynamic waves and particles released in reconnection events can
travel along the magnetic field lines towards the star, which could power the
anomalous ultraviolet flare distribution recently observed in the system. For
an assumed planetary magnetic field of $B_p \simeq 2$ G, we derive the power
released by stellar wind-planet interactions as $\mathcal{P} \sim 10^{22}$ --
$10^{23}$ erg s$^{-1}$, which is consistent with the upper limit of $10^{26}$
erg s$^{-1}$ derived from ultraviolet lines. We further highlight that, because
star-planet interactions depend on stellar wind properties, observations that
probe these interactions and the magnetic map used in 3D stellar wind
simulations should be contemporaneous for deriving realistic results.
