Document Type
Article
Publication Date
2026
Keywords
Navier-Stokes equation, Finite time blowup, Fluid Millennium Prize, Turbulent fluctuations, Newtonian Fluid
Abstract
Non-smooth (finite time blowup) Leray-Hopf solutions of the incompressible Navier-Stokes equation are constructed. The initial data for blowup is characterized by nonzero energy related turbulent fluctuations. The construction occurs in a finite periodic cube T3. The mean value of a weak solution of the Navier-Stokes equation is identified as a smooth solution of the Navier-Stokes equation.
Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.
Recommended Citation
Glimm, James and Petrillo, Jarret, "Non-Smooth Solutions of the Navier-Stokes Equation and their Means" (2026). Department of Applied Mathematics & Statistics Faculty Publications. 18.
https://commons.library.stonybrook.edu/ams-articles/18