Nonlinear Stability of Relativistic Vortex Sheets in Three-Dimensional Minkowski Spacetime

@article{Chen2019NonlinearSO,
  title={Nonlinear Stability of Relativistic Vortex Sheets in Three-Dimensional Minkowski Spacetime},
  author={Gui-Qiang Chen and Paolo Secchi and Tinggui Wang},
  journal={Archive for Rational Mechanics and Analysis},
  year={2019},
  volume={232},
  pages={591-695}
}
We are concerned with the nonlinear stability of vortex sheets for the relativistic Euler equations in three-dimensional Minkowski spacetime. This is a nonlinear hyperbolic problem with a characteristic free boundary. In this paper, we introduce a new symmetrization by choosing appropriate functions as primary unknowns. A necessary and sufficient condition for the weakly linear stability of relativistic vortex sheets is obtained by analyzing the roots of the Lopatinskiĭ determinant associated… CONTINUE READING
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