A new feature in the Notices of the American Mathematical Society explores advances in understanding how shock waves develop in three-dimensional compressible fluids, one of the most challenging problems in modern mathematical physics.

Authored by Leonardo Abbrescia, a former postdoctoral research at Vanderbilt (and now an Assistant Professor at Georgia Tech), and and Jared Speck, a Stevenson Professor of Mathematics at Vanderbilt, the article examines how smooth fluid motion can evolve into singularities that produce shock waves.

Their work connects geometry, partial differential equations, and physics, with implications for areas such as aerospace engineering, weather prediction, and astrophysics.

Read the full article:
https://www.ams.org/journals/notices/202603/rnoti-p185.pdf