4 papers
The Positive Defect Problem: Target and Admissibility Criteria for a Programmatic Search for Unforced Navier-Stokes Blowup
Jarret Petrillo, James Glimm
On 7 and 8 September 2026 programmatic search produced singularities: a forced Navier-Stokes singularity at every fixed viscosity, statements (C) and (D) of the Clay problem, and t…
Smooth Solutions of the Navier-Stokes Equation
James Glimm, Jarret Petrillo
Smooth solutions of the Navier-Stokes equation with smooth but otherwise unconstrained initial conditions are constructed, to solve the Millennium fluids problem in the positive. T…
Non-Smooth Solutions of the Navier-Stokes Equation and their Means
J. Glimm, J. Petrillo
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 re…
Reynolds Averaged Solutions of the Navier-Stokes Equation
James Glimm, Min Chul Lee, Abdul Hasib Rahimyar
The mean of Young measure solutions for the Navier-Stokes equations with general initial conditions are PDE solutions of the Navier-Stokes equation of the class considered by Leray…