대한수학회보 (Bulletin of the Korean Mathematical Society)

  • 제53권2호
  • /
  • Pages.615-640
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  • 2016
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  • 1015-8634(pISSN)
  • /
  • 2234-3016(eISSN)
대한수학회 (Korean Mathematical Society)
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FINITE TIME BLOWUP FOR THE FOURTH-ORDER NLS

  • Cho, Yonggeun (Department of Mathematics and Institute of Pure and Applied Mathematics, Chonbuk National University) ;
  • Ozawa, Tohru (Department of Applied Physics, Waseda University) ;
  • Wang, Chengbo (Department of Mathematics, Zhejiang University)
  • 투고 : 2015.04.11
  • 발행 : 2016.03.31
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초록

We consider the fourth-order $Schr{\ddot{o}}dinger$ equation with focusing inhomogeneous nonlinearity ($-{\mid}x{\mid}^{-2}{\mid}u{\mid}^{\frac{4}{n}}u$) in high space dimensions. Extending Glassey's virial argument, we show the finite time blowup of solutions when the energy is negative.

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참고문헌

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피인용 문헌

  1. A weak form of the soliton resolution conjecture for high-dimensional fourth-order Schrödinger equations vol.14, pp.02, 2017, https://doi.org/10.1142/S0219891617500072