The compressible Euler equations form the cornerstone of fluid dynamics, describing the conservation of mass, momentum and energy in a compressible fluid. When augmented by damping effects, these ...

The Euler equations constitute a fundamental set of hyperbolic partial differential equations that describe the motion of an inviscid fluid. In gas dynamics, these equations are instrumental in ...

In this paper we give a necessary and sufficient condition for the oscillation of the first-order neutral differential equations of Euler form with variable unbounded delays $\tfrac{d} {{dt}}\left( {x ...

A method is given by which one may associate (uniquely) certain differential equations with analytic functions defined by certain Euler product expressions. Some of the consequences of this ...

The plots below illustrate the difference between computations on a moving mesh (left) and a fixed grid (right), both with the same number of grid points. The partial differential differential ...

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 equation in ...