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By incorporating functional analysis and partial differential equation theory from mathematical analysis, this study extends previous investigations on two-dimensional fluid flows to encompass three-dimensional fluid dynamics with axial symmetry conditions.

“When I got my first text on partial differential equations, I learned what love is.”

Many of Caffarelli’s most celebrated results have to do with the regularity — or lack thereof — of the solutions of so-called partial differential equations.

“What you’re trying to figure out is things about the shape of this free boundary,” said Carlos Kenig, a mathematician at the University of Chicago who is also an expert on partial differential equations.

He took four classes toward a bachelor’s degree: partial differential equations, applied numerical methods, mathematics in nature, and number theory and discrete mathematics.