# What's the origin of the naming of Euler equation in economics?

In Economics, Euler equation is:

$$u'(c_{t})=\beta Ru'(c_{t+1})$$

What is the origin of the name of 'Euler' in this equation?

I know that, in fluid dynamics, Euler equation is

\begin{aligned}{D\mathbf {u} \over Dt}&=-\nabla w+\mathbf {g} \\\nabla \cdot \mathbf {u} &=0\end{aligned}

However, I cannot catch the similarity between economics and fluid dynamics for the Euler equation.

• There are dozens, if not hundreds, of Euler equations/identities/theorems in math, physics, engineering, economics, etc. It shouldn't be too surprising that there is another Euler equation in fluid dynamics. Dec 1 '21 at 15:04
• My guess is that it came from the Euler-Lagrange equation in calculus of variation. When you are doing utility maximization in continuous time, you are basically doing constrained calculus of variation, aka optimal control. Dec 1 '21 at 15:08