Context :

Aims : We aim to study the influence of radiative cooling on the standing kink oscillations of a coronal loop .

Methods : Using the FLASH code , we solve the 3D ideal MHD equations .
Our model consists of a straight , density enhanced and gravitationally stratified magnetic flux tube .
We perturb the system initially , leading to a transverse oscillation of the structure , and follow its evolution for a number of periods .
A realistic radiative cooling is implemented .
Results are compared to available analytical theory .

Results : We find that in the linear regime ( i.e .
low amplitude perturbation and slow cooling ) the obtained period and damping time are in a good agreement with theory .
The cooling leads to an amplification of the oscillation amplitude .
However , the difference between the cooling and non-cooling cases is small ( around 6 % after 6 oscillations ) .
In high amplitude runs with realistic cooling , instabilities deform the loop , leading to increased damping .
In this case , the difference between cooling and non-cooling is still negligible , around 12 % .
A set of simulations with higher density loops are also performed , to explore what happens when the cooling takes place in a very short time ( t _ { \mathrm { cool } } \approx 100 s ) .
In this case , the difference in amplitude after nearly 3 oscillation periods for the low amplitude case is 21 % between cooling and non-cooling cases .
We strengthen the results of previous analytical studies stating that the amplification due to cooling is ineffective , and its influence on the oscillation characteristics is small , at least for the cases shown here .
Furthermore , the presence of a relatively strong damping in the high amplitude runs even in the fast cooling case indicates that it is unlikely that cooling could account alone for the observed , flare related undamped oscillations of coronal loops .
These results may be significant in the field of coronal seismology , allowing its application to coronal loop oscillations with observed fading-out or cooling behaviour .

Conclusions :