The Boson star equation with initial data of low regularity
arXiv:1305.6392 · doi:10.1016/j.na.2013.11.023
Abstract
The Cauchy problem for the L^2-critical boson star equation with initial data of low regularity in spatial dimension d=3 is studied. Local well-posedness in H^s for s > 1/4 is proved. Moreover, for radial initial data, local well-posedness is established in H^s for s > 0. Both results are shown to be almost optimal by providing complementary ill-posedness results.
v2: referee's comments incorporated; proof of Prop. 2.4 corrected; note that in the non-radial case Prop. 2.4 and Theorem 1.1 (i) is restricted to s>1/4
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