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 ...
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 ...
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 ...
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 ...
Helicity is, like energy, a quadratic invariant of the Euler equations of ideal fluid flow, although, unlike energy, it is not sign definite. In physical terms, it represents the degree of linkage of ...
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 ...
Mathematicians have suspected for years that under specific circumstances, the Euler equations fail. But they've been unable to identify an exact scenario in which this failure occurs. Until now. The ...
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