6 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…
Construction of Nontrivial Quantum Gauge Theories: The Continuum limit in a Finite Volume
James Glimm, Jarret Petrillo, Min Chul Lee
We construct several quantum gauge theories in 4 dimensional space time, including both Abelian and non Abelian gauge groups, with the Abelian gauge fields coupled to zero mass mat…
Verification and Validation of Log-Periodic Power Law Models
Jarret Petrillo
We propose and implement a nonlinear Verification and Validation (V&V) methodology to test two fitting procedures for the log-periodic power law model (LPPL), a model that has dive…
Kubo Combinatorics for Turbulence Scaling Laws
Jarret Petrillo, James Glimm
We present an extension to Kolmogorov's refined similarity hypothesis for universal fully developed turbulence. The extension is applied within Z. She and E. Leveque's multifractal…