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On the incompressible fluid limit and the vortex motion law of the nonlinear Schrdinger equation

F-H Lin Jack Xin

Analysis of PDEs mathscidoc:1912.43841

Communications in mathematical physics, 200, (2), 249-274, 1999.2
The nonlinear Schrdinger equation (NLS) has been a fundamental model for understanding vortex motion in superfluids. The vortex motion law has been formally derived on various physical grounds and has been around for almost half a century. We study the nonlinear Schrdinger equation in the incompressible fluid limit on a bounded domain with Dirichlet or Neumann boundary condition. The initial condition contains any finite number of degree 1 vortices. We prove that the NLS linear momentum weakly converges to a solution of the incompressible Euler equation away from the vortices. If the initial NLS energy is almost minimizing, we show that the vortex motion obeys the classical Kirchhoff law for fluid point vortices. Similar results hold for the entire plane and periodic cases, and a related complex GinzburgLandau equation. We treat as well the semi-classical (WKB) limit of NLS in the presence of
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@inproceedings{f-h1999on,
  title={On the incompressible fluid limit and the vortex motion law of the nonlinear Schrdinger equation},
  author={F-H Lin, and Jack Xin},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210130394794405},
  booktitle={Communications in mathematical physics},
  volume={200},
  number={2},
  pages={249-274},
  year={1999},
}
F-H Lin, and Jack Xin. On the incompressible fluid limit and the vortex motion law of the nonlinear Schrdinger equation. 1999. Vol. 200. In Communications in mathematical physics. pp.249-274. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191224210130394794405.
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