English

The Boson star equation with initial data of low regularity

Analysis of PDEs 2013-12-12 v2

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.

Keywords

Cite

@article{arxiv.1305.6392,
  title  = {The Boson star equation with initial data of low regularity},
  author = {Sebastian Herr and Enno Lenzmann},
  journal= {arXiv preprint arXiv:1305.6392},
  year   = {2013}
}

Comments

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

R2 v1 2026-06-22T00:23:35.441Z