Context :

Aims : We model the effects of the spiral arms of the Milky Way on the disk stellar kinematics in the Gaia observable space .
We also estimate the Gaia capabilities of detecting the predicted signatures .

Methods : We use both controlled orbital integrations in analytic potentials and self-consistent simulations .
We introduce a new strategy to investigate the effects of spiral arms , which consists of comparing the stellar kinematics of symmetric Galactic longitudes ( + l and - l ) , in particular the median transverse velocity as determined from parallaxes and proper motions .
This approach does not require the assumption of an axisymmetric model because it involves an internal comparison of the data .

Results : The typical differences between the transverse velocity in symmetric longitudes in the models are of the order of \sim 2 { km s ^ { -1 } } , but can be larger than 10 { km s ^ { -1 } } for certain longitudes and distances .
The longitudes close to the Galactic centre and to the anti-centre are those with larger and smaller differences , respectively .
The differences between the kinematics for + l and - l show clear trends that depend strongly on the properties of spiral arms .
Thus , this method can be used to quantify the importance of the effects of spiral arms on the orbits of stars in the different regions of the disk , and to constrain the location of the arms , main resonances and , thus , pattern speed .
Moreover , the method allows us to test different origin scenarios of spiral arms and the dynamical nature of the spiral structure ( e.g .
grand design versus transient multiple arms ) .
We estimate the number of stars of each spectral type that Gaia will observe in certain representative Galactic longitudes , their characteristic errors in distance and transverse velocity , and the error in computing the median velocity as a function of distance .
We will be able to measure the median transverse velocity exclusively with Gaia data , with precision smaller than \sim 1 { km s ^ { -1 } } up to distances of \sim 4 - 6 { kpc } for certain giant stars , and up to \sim 2 - 4 { kpc } and better kinematic precision ( \lesssim 0.5 { km s ^ { -1 } } ) for certain sub-giants and dwarfs .
These are enough to measure the typical signatures seen in the models .

Conclusions : The Gaia catalogue will allow us to use the presented approach successfully and improve significantly upon current studies of the dynamics of the spiral arms of our Galaxy .
We also show that a similar strategy can be used with line-of-sight velocities , which could be applied to Gaia data and to upcoming spectroscopic surveys .