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 ...
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 ...
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, ...
In this note, we rigorously justify a singular approximation of the incompressible Navier-Stokes equations. Our approximation combines two classical approximations of the incompressible Euler ...
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 ...
1. Fluid Mechanics II (MECH 361), 3.5 Credits: Differential analysis of fluid flows, vorticity, stream function, stresses, and strains. Navier-Stokes equations and solutions for parallel flows.
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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