Camillo De Lellis
Princeton University, NJ·Mathematics & Statistics
The equations describing fluid motion are centuries old. Yet mathematicians still cannot fully explain some basic behaviors of their solutions.
- Fields
Mathematics & Statistics
Physics
- Topics
partial differential equations
fluid dynamics
incompressible flow
- Grants
- 1 known grant, through Jul 2027
What they work on
- Prove the existence of Navier-Stokes solutions whose kinetic energy dissipation stays positive as viscosity goes to zero, without adding spurious oscillations to the initial data, giving rigorous examples of anomalous dissipation.
- Investigate whether smooth solutions of the incompressible Navier-Stokes and Euler equations can blow up, developing singularities in finite time.
- Study simpler model cases, such as anomalous dissipation driven by forcing terms and deformed Navier-Stokes equations within a larger family, as steps toward the full problems.
More about the research
A central puzzle concerns turbulence. Experiments show that turbulent flows keep losing kinetic energy even as the fluid's viscosity (its internal friction) shrinks toward zero. But smooth solutions of the zero-viscosity equations can be proven to conserve energy. This project starts from that contradiction to study the regularity (smoothness), uniqueness and stability of fluid flow solutions.
Why it matters
This is basic mathematical research. Rigorous results on energy loss and possible blow-up in fluid equations would help explain turbulence, a phenomenon common throughout science and engineering. It could eventually inform how scientists understand and model turbulent fluid flows.
Known grants
From NIH and NSF research grants. Labs often have other funding we can't see.
Closest labs
Theodore Drivas
Stony Brook University, NY·Mathematics & Statistics·Early-career
Analyze the long-time behavior of the two-dimensional Euler equations to explain how ideal fluids form lasting, hurricane-like vortices through vortex merging and mixing.
Zachary Bradshaw
University of Arkansas, AR·Mathematics & Statistics
Analyze the dynamic stability of multi-celled vortex solutions of the Navier-Stokes equations, such as tornado-like models with an updraft surrounding a central downdraft.
Dionyssios Mantzavinos
University of Kansas, KS·Mathematics & Statistics
Develop analytical tools to establish existence, uniqueness and stability of solutions to nonlinear partial differential equations posed in bounded domains in two or more spatial dimensions.
The school
Princeton University: 26 labs on PI Pages, $559M a year on research, 403 research doctorates a year.
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