Louis Nirenberg

Louis Nirenberg is one of the outstanding mathematicians of the 20th century, who made fundamental contributions to the theory of partial differential equations. In the context of the Navier–Stokes problem, he is a co-author of the Caffarelli–Kohn–Nirenberg theorem (1982), which established partial regularity of suitable weak solutions: the singular set has zero one-dimensional Hausdorff measure. This theorem became an important tool in the study of possible blow-up of solutions. Nirenberg is also known for his work on interpolation inequalities (the Gagliardo–Nirenberg inequality), elliptic equations, and geometric analysis, for which he was awarded the Abel Prize in 2015.

Biography

Louis Nirenberg was born in Hamilton, Canada, in 1925. He received his bachelor's degree from McGill University and his doctorate from New York University in 1949 under the supervision of James Stoker. His entire career was associated with the Courant Institute of New York University, where he became a professor and director. Among his awards are the Bôcher Prize (1959), the Crafoord Prize (1982), the National Medal of Science (1995), the Steele Prize (1994), and the Abel Prize (2015).

Key discoveries

Together with Caffarelli and Kohn, proved partial regularity of suitable weak solutions of Navier–Stokes (1982).
Derived the Gagliardo–Nirenberg inequality, widely used in the theory of partial differential equations.
Contributed to the theory of elliptic equations, including regularity of solutions and maximum principles.

Biography

Key discoveries

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