Annales Henri Poincaré

, Volume 20, Issue 7, pp 2173–2270 | Cite as

The Relativistic Euler Equations: Remarkable Null Structures and Regularity Properties

  • Marcelo M. DisconziEmail author
  • Jared Speck


We derive a new formulation of the relativistic Euler equations that exhibits remarkable properties. This new formulation consists of a coupled system of geometric wave, transport, and transport-div-curl equations, sourced by nonlinearities that are null forms relative to the acoustical metric. Our new formulation is well-suited for various applications, in particular, for the study of stable shock formation, as it is surveyed in the paper. Moreover, using the new formulation presented here, we establish a local well-posedness result showing that the vorticity and the entropy of the fluid are one degree more differentiable compared to the regularity guaranteed by standard estimates (assuming that the initial data enjoy the extra differentiability). This gain in regularity is essential for the study of shock formation without symmetry assumptions. Our results hold for an arbitrary equation of state, not necessarily of barotropic type.

Mathematics Subject Classification

35Q75 Secondary 35L10 35Q35 35L67 



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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Vanderbilt UniversityNashvilleUSA
  2. 2.Massachusetts Institute of TechnologyCambridgeUSA

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