Luis Ángel Caffarelli (Spanish pronunciation: [ˈlwis anˈxel kaffaˈɾeʎi]; born December 8, 1948) is an Argentine-American[3] mathematician.

[5][6] He currently holds the Sid Richardson Chair at the University of Texas at Austin and is core faculty at the Oden Institute for Computational Engineering and Sciences.

Caffarelli published "The regularity of free boundaries in higher dimensions" in 1977 in Acta Mathematica.

[8] One of his most cited results regards the Partial regularity of suitable weak solutions of the Navier–Stokes equations; it was obtained in 1982 in collaboration with Louis Nirenberg and Robert V.

In 2005, he received the prestigious Rolf Schock Prize of the Royal Swedish Academy of Sciences "for his important contributions to the theory of nonlinear partial differential equations".