International audienceTo prepare the microgravity experiment of crystal growth by floating zone method, GEZON, numerical studies of hydrodynamics of the melt are carried out. Calculations of zone length and convection driven by surface-tension gradients are presented for germanium floating zone operating under microgravity conditions. Results of linear stability analysis show the instability of intense thermocapillarity convection needed to be damped by using a magnetic field; the critical magnetic induction is obtained. it is expected to grow a striation-free crystal with this magnetic fiel