The Boson star equation with initial data of low regularity

The Cauchy problem for the L2L2-critical boson star equation with initial data of low regularity in spatial dimension d=3d=3 is studied. Local well-posedness in HsHs for s>1/4s>1/4 is proved. Moreover, for radial initial data, local well-posedness is established in HsHs for s>0s>0. Both results are shown to be almost optimal by providing complementary ill-posedness results.