“Gentlemen, that is surely true, it is absolutely paradoxical; we cannot understand it, and we don’t know what it means. But we have proved it, and therefore we know it must be the truth.” —Benjamin ...

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 ...

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 ...

Purdue faculty dedicate countless hours to exploring the frontiers of their respective fields, pushing the boundaries of knowledge and contributing to the ever-evolving landscape of academia. To ...

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 ...

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 ...

The cosmos is a unique laboratory for testing the laws of physics, in particular those of Euler and Einstein. Euler described the movements of celestial objects, while Einstein described the way in ...

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 ...

A recent entry in the visitor’s book of the James Joyce Tower & Museum in Sandycove, Dublin, perplexed the Friends of Joyce’s Tower, the volunteers who run the museum. The entry, reproduced as the ...