Blow-Up for Nonlinear Wave Equations describing Boson Stars

@inproceedings{Froehlich2005BlowUpFN,
  title={Blow-Up for Nonlinear Wave Equations describing Boson Stars},
  author={Juerg Froehlich and Enno Lenzmann},
  year={2005}
}
We consider the nonlinear wave equation i∂tu = √ −∆ + mu − (|x| ∗ |u|2)u on R modelling the dynamics of (pseudo-relativistic) boson stars. For spherically symmetric initial data, u0(x) ∈ C ∞ c (R ), with negative energy, we prove blowup of u(t, x) in H-norm within a finite time. Physically, this phenomenon describes the onset of “gravitational collapse” of a boson star. We also study blow-up in external, spherically symmetric potentials and we consider more general Hartree-type nonlinearities… CONTINUE READING

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