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 ...

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 ...

A $1 million prize awaits anyone who can show where the math of fluid flow breaks down. With specially trained AI systems, ...

Shock formation represents the process whereby smooth solutions to the governing equations of fluid dynamics undergo a transition to discontinuous states. In compressible fluid dynamics, this ...

Scientific progress is not usually straightforward. Researchers pursue and abandon lines of inquiry. Results languish. Theories take decades to cohere. But sometimes the accumulation of scientific ...

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 ...

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 ...