Non-Smooth Solutions of the Navier-Stokes Equation and their Means
arXiv:2410.09261
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.
This has been merged with arXiv 2505.13816v2. Identification of Millennium fluids prize corrected and other minor changes