This work is devoted to the stationary solutions of the 2D Euler equations describing the time-independent flows of an ideal incompressible fluid. There exists an infinite-dimensional set of such ...

The partial differential differential equations being solved are the Euler equations of gasdynamics: with piecewise constant initial conditions (also known as Sod's shock tube problem ). The ...

To model the motion of a more realistic fluid with internal friction (or viscosity), researchers use the Navier-Stokes equations instead. “The Euler equations are very idealized. Real fluids have ...

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 ...

For more than 250 years, mathematicians have wondered if the Euler equations might sometimes fail to describe a fluid’s flow. Now there’s a breakthrough.

The theories of Leonhard Euler (1707-1783) and Albert Einstein (1879-1955) revolutionised our understanding of the Universe. With the famous equation that bears his name, Euler gave scientists a ...

In fact, this equation, familiar to mathematicians and greatly admired for its elegance, is known as Euler’s Identity. Mathematician Leonhard Euler, born in Switzerland in 1707, spent most of ...