The Mathematician Who Found Where Navier–Stokes Could Break

Luis Caffarelli transformed the study of partial differential equations by learning how to distinguish smooth behavior from singularity. After moving from Buenos Aires to Minnesota, a problem from Hans Lewy led him to free boundaries and his landmark 1977 regularity theorem. At Courant he joined Robert Kohn and Louis Nirenberg to prove the 1982 CKN theorem, sharply restricting possible Navier–Stokes singularities. Later breakthroughs on nonlinear equations and Monge–Ampère theory led to the 2023 Abel Prize.

Caffarelli's mathematics tackles a deceptively simple question: when equations model the physical world, how can we know their solutions stay well behaved? His work on obstacle problems showed how apparently irregular boundaries can become smooth, while the CKN theorem proved that any singularities in suitable Navier–Stokes solutions must be exceptionally small. He never solved the Millennium Problem itself; instead, he built some of the strongest tools for approaching it and reshaped regularity theory across nonlinear.