Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrdinger equations

Michael I Weinstein Jack Xin

Analysis of PDEs mathscidoc:1912.43859

Communications in mathematical physics, 180, (2), 389-428, 1996.10
The dynamic stability of vortex solutions to the Ginzburg-Landau and nonlinear Schrdinger equations is the basic assumption of the asymptotic particle plus field description of interacting vortices. For the Ginzburg-Landau dynamics we prove that all vortices are asymptotically nonlinearly stable relative to small radial perturbations. Initially finite energy perturbations of vortices decay to zero in<i>L</i> <sup> <i>p</i> </sup>(<sup>2</sup>) spaces with an algebraic rate as time tends to infinity. We also prove that under general (nonradial) perturbations, the plus and minus one-vortices are linearly dynamically stable in<i>L</i> <sup>2</sup>; the linearized operator has spectrum equal to (, 0] and generates a<i>C</i> <sub>0</sub> semigroup of contractions on<i>L</i> <sup>2</sup>(<sup>2</sup>). The nature of the zero energy point is clarified; it is<i>resonance</i>, a property related to the infinite energy of planar vortices. Our results on the linearized operator are also used to show that the plus and
No keywords uploaded!
[ Download ] [ 2019-12-24 21:02:42 uploaded by Jack_Xin ] [ 233 downloads ] [ 0 comments ]
@inproceedings{michael1996dynamic,
  title={Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrdinger equations},
  author={Michael I Weinstein, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210242707246423},
  booktitle={Communications in mathematical physics},
  volume={180},
  number={2},
  pages={389-428},
  year={1996},
}
Michael I Weinstein, and Jack Xin. Dynamic stability of vortex solutions of Ginzburg-Landau and nonlinear Schrdinger equations. 1996. Vol. 180. In Communications in mathematical physics. pp.389-428. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210242707246423.
Please log in for comment!
 
 
Contact us: office-iccm@tsinghua.edu.cn | Copyright Reserved