Euler’s identity is an equality found in mathematics that has been compared to a Shakespearean sonnet and described as "the most beautiful equation." It is a special case of a foundational ...

The Euler and Navier-Stokes equations form the cornerstone of fluid dynamics, governing the motion of fluids under a wide range of conditions. The Euler equations describe inviscid flows where ...

Perhaps the oldest and most prominent of these equations, formulated by Leonhard Euler more than 250 years ago, describe the flow of an ideal, incompressible fluid: a fluid with no viscosity, or ...

The subject was then developed by a method of "synthesis" by systematically applying Newton's laws to fluid elements culminating in the fundamental equations of fluid flow — the Euler system of ...

But we have proved it, and therefore we know it must be the truth.” —Benjamin Pierce, a Harvard mathematician, after proving Euler’s equation, ei p = –1, in a 19th-century lecture.

Euler’s identity is a special case of a foundational equation in complex analysis, Euler’s Formula, which he discovered in 1744. It shows how any complex number can be obtained by rotating a ...

For the past 20 years, Professor Masmoudi’s research has been at the forefront of Partial Differential Equations, Fluid Mechanics, and Dynamical Systems.