[en] For the Inertial Confinement Fusion, the different problems to be studied are: DT burning, shell implosion and hydrodynamic instabilities, spherical symmetry of the shell given by the X-rays produced in a hohlraum and laser-plasma interaction. One of the requirements is that the shell stay essentially spherical up to the end of the implosion. In these conditions, 2-D simulations show a gain of 10 in a realistic configuration. The Rayleigh-Taylor instabilities occurring during the shell implosion grow first in the linear regime for which we have some models and experimental results. But the saturation mechanism reduces the final amplitude significantly. By using a simple but global model, we determine an operating domain of the LMJ, taking into account a 25% margin for laser energy. (author)