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


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Article Info

DATE

2019-05

AUTHORS

Gui-Qiang G. Chen, Paolo Secchi, Tao Wang

ABSTRACT

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 to the constant coefficient linearized problem. Under this stability condition, we show that the variable coefficient linearized problem obeys an energy estimate with a loss of derivatives. The construction of certain weight functions plays a crucial role in absorbing the error terms caused by microlocalization. Based on the weakly linear stability result, we establish the existence and nonlinear stability of relativistic vortex sheets under small initial perturbations by a Nash–Moser iteration scheme. More... »

PAGES

591-695

References to SciGraph publications

  • 2012. Nonlinear Partial Differential Equations, The Abel Symposium 2010 in NONE
  • 1976-03. The boundary problems of physical geodesy in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2018-05. Local Existence of MHD Contact Discontinuities in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2006-03. Blowup of Smooth Solutions for Relativistic Euler Equations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 1996-06. Well-posedness of characteristic symmetric hyperbolic systems in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2009-02. The Existence of Current-Vortex Sheets in Ideal Compressible Magnetohydrodynamics in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1993-09. Global solutions of the relativistic Euler equations in COMMUNICATIONS IN MATHEMATICAL PHYSICS
  • 2015-04. Weak stability of transonic contact discontinuities in three-dimensional steady non-isentropic compressible Euler flows in ZEITSCHRIFT FÜR ANGEWANDTE MATHEMATIK UND PHYSIK
  • 1959-01. On circulation in relativistic hydrodynamics in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2013-05. Stabilization Effect of Magnetic Fields on Two-Dimensional Compressible Current-Vortex Sheets in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 2008-03. Existence and Stability of Compressible Current-Vortex Sheets in Three-Dimensional Magnetohydrodynamics in ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS
  • 1972. Non-Homogeneous Boundary Value Problems and Applications, Vol. 1 in NONE
  • Identifiers

    URI

    http://scigraph.springernature.com/pub.10.1007/s00205-018-1330-5

    DOI

    http://dx.doi.org/10.1007/s00205-018-1330-5

    DIMENSIONS

    https://app.dimensions.ai/details/publication/pub.1107912133


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