Large data mass-subcritical NLS: critical weighted bounds imply scattering

@article{Killip2016LargeDM,
  title={Large data mass-subcritical NLS: critical weighted bounds imply scattering},
  author={R. Killip and Satoshi Masaki and J. Murphy and M. Visan},
  journal={Nonlinear Differential Equations and Applications NoDEA},
  year={2016},
  volume={24},
  pages={1-33}
}
We consider the mass-subcritical nonlinear Schrödinger equation in all space dimensions with focusing or defocusing nonlinearity. For such equations with critical regularity $$s_c\in (\max \{-1,-\frac{d}{2}\},0)$$sc∈(max{-1,-d2},0), we prove that any solution satisfying $$\begin{aligned} \left\| \, |x|^{|s_c|}e^{-it\Delta } u\right\| _{L_t^\infty L_x^2} <\infty \end{aligned}$$|x||sc|e-itΔuLt∞Lx2<∞on its maximal interval of existence must be global and scatter. 
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  • 2
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  • 2
  • Highly Influenced
  • PDF
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  • PDF
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  • 3
  • PDF
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  • 1
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References

SHOWING 1-10 OF 63 REFERENCES
The focusing energy-critical nonlinear Schrödinger equation in dimensions five and higher
  • 189
  • PDF
CONVERGENCE TO SCATTERING STATES IN THE NONLINEAR SCHRÖDINGER EQUATION
  • 7
  • PDF
Remarks on scattering for nonlinear Schrödinger equations
  • 71
Mass concentration phenomena for the $L^2$-critical nonlinear Schrödinger equation
  • 127
  • PDF
Global well-posedness and scattering for the higher-dimensional energy-critical non-linear Schrodinger equation for radial data
  • T. Tao
  • Physics, Mathematics
  • 2004
  • 121
  • PDF
A sharp scattering condition for focusing mass-subcritical nonlinear Schr\"odinger equation
  • 14
  • PDF
The mass-critical nonlinear Schr\"odinger equation with radial data in dimensions three and higher
  • 135
  • PDF
...
1
2
3
4
5
...