This Project Grant award from the National Science Foundation (NSF) under the Mathematical and Physical Sciences (CFDA 47.049) program provides $257,048 to New York University (NYU) to conduct research on singularities in fluid dynamics. The key research components include: 1) Providing a full description of shock wave formation and development for multi-dimensional compressible Euler equations, 2) Further developing prior work on self-similar imploding solutions for isentropic compressible flows to investigate new types of singularities, and 3) Utilizing physically informed neural networks to search for new forms of singularities in fluid dynamics with the aid of computer-assisted proofs. The award will also support research opportunities and training for postdoctoral scholars, as well as the development of a graduate textbook on shock waves in compressible fluids. The project period runs from April 2024 through August 2027.
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