The new international facility for antiproton and ion research (FAIR), at Darmstadt, Germany, will accelerate beams of all stable isotopes from protons up to uranium with unprecedented intensities (of the order of 1012 ions per spill). Planned future experiments include production of exotic nuclei by fragmentation/fission of projectile ions of different species with energies up to 1.5 GeV/u at the proposed super conducting fragment separator, Super-FRS. In such experiments, the production target must survive multiple irradiations over an extended period of time, which in case of such beam intensities is highly questionable. Previous work showed that with full intensity of the uranium beam, a solid graphite target will be destroyed after being irradiated once, unless the beam focal spot is made very large that will result in extremely poor transmission and resolution of the secondary isotopes. An alternative to a solid target could be a windowless liquid jet target. We have carried out three-dimensional numerical simulations to study the problem of target heating and propagation of pressure in a liquid Li target. These first calculations have shown that a liquid lithium target may survive the full uranium beam intensity for a reasonable size focal spot.