Editing Euler equations (fluid dynamics) (section)

==History==
The Euler equations first appeared in published form in Euler's article "Principes généraux du mouvement des fluides", published in ''Mémoires de l'Académie des Sciences de Berlin'' in 1757{{sfn|Euler|1757}} (although Euler had previously presented his work to the Berlin Academy in 1752).{{sfn|Christodoulou|2007|p=}} Prior work included contributions from the [[Bernoulli family]] as well as from [[Jean le Rond d'Alembert]].<ref>{{Cite journal |last1=Darrigol |first1=O. |last2=Frisch |first2=U. |date=2008 |title=From Newton's mechanics to Euler's equations |url=https://linkinghub.elsevier.com/retrieve/pii/S0167278907002886 |journal=Physica D: Nonlinear Phenomena |language=en |volume=237 |issue=14–17 |pages=1855–1869 |doi=10.1016/j.physd.2007.08.003|bibcode=2008PhyD..237.1855D |url-access=subscription }}</ref>

The Euler equations were among the first [[partial differential equations]] to be written down, after the [[wave equation]]. In Euler's original work, the system of equations consisted of the momentum and continuity equations, and thus was underdetermined except in the case of an incompressible flow. An additional equation, which was called the [[Adiabatic process|adiabatic condition]], was supplied by [[Pierre-Simon Laplace]] in 1816.

During the second half of the 19th century, it was found that the equation related to the balance of energy must at all times be kept for compressible flows, and the adiabatic condition is a consequence of the fundamental laws in the case of smooth solutions. With the discovery of the [[special theory of relativity]], the concepts of energy density, momentum density, and stress were unified into the concept of the [[stress–energy tensor]], and energy and momentum were likewise unified into a single concept, the [[Four-momentum|energy–momentum vector]].{{sfn|Christodoulou|2007|p=}}