  In the quest to solve the long-standing coronal heating problem, it has been
suggested half a century ago that coronal loops could be heated by waves.
Despite the accumulating observational evidence of the possible importance of
coronal waves, still no 3D MHD simulations exist that show significant heating
by MHD waves. Here we report on the first 3D coronal loop model heating the
plasma against radiative cooling. The coronal loop is driven at the footpoint
by transverse oscillations and subsequently the induced Kelvin-Helmholtz
instability deforms the loop cross-section and generates small-scale
structures. Wave energy is transfered to smaller scales where it is dissipated,
overcoming the internal energy losses by radiation. These results open up a new
avenue to address the coronal heating problem.
