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...The euler equation of gas dynamics a mignone october in this lecture we study some properties equations gasdynamics u t p where and denote that density pressure bulk velocity last can be recovered from internal energy see next section assuming an ideal which satises e is specic heat ratio order to derive for start conservative form total now consider temporal evolution kinetic term using momentum eq obtain tu wecannowreplacethe second square bracket vector identity so together with continuity previous reads substituting eu represents work done by compression or expansion relation st law thermodynamics notice actually rst just written dierent way prove equivalence directly our notations as de pdv q adiabatic v volume divided mass holds uid it moves along streamline after dividing dt derivatives must understood convective lagrangian derivative d one obtains multiplication gives again adierent obtained rd thas terms simplify left s ds simply states conservation entropy reecting nature den...