For anyone fascinated by powers and integers, there’s no shortage of problems to tackle, whether by ingenious logic or massive computer search. In 1769, while thinking about the problem now known as ...

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 ...

TUCSON, March 19 (UPI) -- U.S. scientists Daniel Madden and Lee Jacobi have solved "Euler's equation of degree four" -- a puzzle that has stymied scientists for centuries. Madden, a University of ...

For centuries, mathematicians have sought to understand and model the motion of fluids. The equations that describe how ripples crease the surface of a pond have also helped researchers to predict the ...

Journal of Computational Mathematics, Vol. 22, No. 2, SPECIAL ISSUE DEDICATED TO THE 70TH BIRTHDAY OF PROFESSOR ZHONG-CI SHI (MARCH 2004), pp. 220-229 (10 pages) In this paper, we perform a nonlinear ...

Billy Hudson, a mathematician, writes, "I was in a introductory Number Theory class when Professor David Ferguson told me that e^(ipi) + 1 = 0. Of course, Euler's equation had the same affect on me as ...

Many people find complex math puzzling, including some mathematicians. Recently, a mathematician has found solutions to a puzzle that has been around for centuries. They have found a way to generate ...

We prove existence on infinite time intervals of regular solutions to the 3D Navier-Stokes equations for fully three-dimensional initial data characterized by uniformly large vorticity; smoothness ...