The National Science Foundation awarded a $360,000 Project Grant to the University of Illinois for the project "Pathological Solutions of Fluid Equations". The grant period runs from June 1, 2023 to May 31, 2026.
The project will study fundamental open questions concerning the equations of fluid motion, which are widely used in physics and engineering applications. The research aims to demonstrate limitations in the notion of "weak solutions" to these equations, which have been extensively used by mathematicians, by constructing weak solutions with unphysical properties. Conversely, the project proposes to prove the existence of physical solutions that can better describe turbulent fluid flows. The research will also provide graduate student research opportunities.
This award aligns with the National Science Foundation's Mathematical and Physical Sciences program (CFDA 47.049), which supports scientific research to increase the store of knowledge and enhance understanding of major problems facing the nation.
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