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- W2035045829 abstract "We prove local and global well-posedness for semi-relativistic, nonlinear Schrödinger equations $i partial_t u = sqrt{-Delta + m^2} u + F(u)$ with initial data in H s (ℝ3), $s geqslant 1/2$ . Here F(u) is a critical Hartree nonlinearity that corresponds to Coulomb or Yukawa type self-interactions. For focusing F(u), which arise in the quantum theory of boson stars, we derive global-in-time existence for small initial data, where the smallness condition is expressed in terms of the L 2-norm of solitary wave ground states. Our proof of well-posedness does not rely on Strichartz type estimates. As a major benefit from this, our method enables us to consider external potentials of a quite general class." @default.
- W2035045829 created "2016-06-24" @default.
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- W2035045829 date "2007-05-26" @default.
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- W2035045829 title "Well-posedness for Semi-relativistic Hartree Equations of Critical Type" @default.
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- W2035045829 doi "https://doi.org/10.1007/s11040-007-9020-9" @default.
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