Robert V. Kohn

Robert Kohn is an American mathematician specializing in the calculus of variations, differential equations, and materials science. In the context of the Navier–Stokes equations, he is known as a co-author of the 1982 Caffarelli–Kohn–Nirenberg theorem, which proved partial regularity of suitable weak solutions. This theorem states that the singular set of such solutions has zero one-dimensional Hausdorff measure, limiting possible blow-up points. Kohn also made significant contributions to the theory of phase transitions, micromagnetics, and the analysis of microstructures in materials.

Biography

Robert Kohn was born in 1953. He received his bachelor's degree from Harvard University and his Ph.D. from Princeton University in 1979 under the supervision of Frederick Almgren. He worked at the Courant Institute of Mathematical Sciences at New York University, where he is a professor. He has supervised many notable mathematicians, including Sylvia Serfaty.

Key discoveries

Together with Caffarelli and Nirenberg, proved partial regularity of suitable weak solutions of Navier–Stokes (1982).
Developed relaxation theory for nonconvex variational problems, important for modeling microstructures in materials.
Contributed to the analysis of phase transition models such as the Cahn–Hilliard functional.

Biography

Key discoveries

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