Global solutions to the relativistic Euler equation with spherical symmetry
type: Item
instance of: scholarly article
title: Global solutions to the relativistic Euler equation with spherical symmetry
zbMATH Open document ID: 0879.35155
DOI: 10.1007/BF03167315
author: Kiyoshi Mizohata
published in: Japan Journal of Industrial and Applied Mathematics
publication date: 1997-08-28T00:00:00Z
review text: The relativistic Euler equation in \(\mathbb{R}^3\) is given by \[ {\partial\over\partial t} \Biggl({\rho c^2+P\over c^2} {1\over 1-{v^2\over c^2}}-{P\over c^2}\Biggr)+ \sum^3_{j=1} {\partial\over\partial x_j} \Biggl({\rho c^2+P\over c^2} {v_j\over 1-{v^2\over c^2}}\Biggr)=0, \] \[ {\partial\over\partial t} \Biggl({\rho c^2+P\over c^2} {v_i\over 1-{v^2\over c^2}}\Biggr)+ \sum^3_{j=1} {\partial\over\partial x_j} \Biggl({\rho c^2+P\over c^2} {v_iv_j\over 1-{v^2\over c^2}}+\delta_{ij}P\Biggr)= 0,\;i=1,2,3. \] In 1993, Smoller and Temple have constructed global weak solutions to this equation in the one-dimensional case. In this article we show the existence of global weak solutions with spherical symmetry.
Mathematics Subject Classification ID: 35Q75
Mathematics Subject Classification ID: 35Q15
Mathematics Subject Classification ID: 35D05
zbMATH DE Number: 1054333
zbMATH Keywords: Riemann problem
zbMATH Keywords: Glimm's method
zbMATH Keywords: relativistic Euler equation
zbMATH Keywords: existence of global weak solutions with spherical symmetry
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1054333