15 papers
Filtered Vortex Stretching and Subgrid Defects for the Three-Dimensional Navier-Stokes Equations
Runlong Yu
We prove a finite-scale estimate for vortex stretching in spatially filtered three-dimensional Navier--Stokes flow. The positive near-field part of the filtered stretching is bound…
A Structural Audit of Navier-Stokes Obstruction Calculus
Runlong Yu
We audit a finite-scale program for the local regularity problem of the three-dimensional incompressible Navier--Stokes equations. The program develops critical ledgers, coarse-gra…
Coarse-Grained Resolution and Pressure-Flux Work Depletion for Navier-Stokes CKN Badness
Runlong Yu
We prove a finite-scale coarse-grained decomposition for the three-dimensional incompressible Navier-Stokes equations near the Caffarelli-Kohn-Nirenberg local regularity framework.…
Finite-Chain CKN-Bad Scale Counting for Navier-Stokes: Standard PDE Closure and Canonical Detector Realization
Runlong Yu
This paper proves a finite-chain counting theorem for Caffarelli--Kohn--Nirenberg bad scales of suitable weak solutions to the three-dimensional incompressible Navier--Stokes equat…
Physics-Preserving Latent Compression for Zero-Shot Resolution Transfer in 3D Turbulence
Yilong Dai, Yiming Sun, Yiheng Chen +4
High-resolution turbulence modeling is essential for scientific computing, but remains constrained by the cost of direct numerical simulation and the scarcity of full-resolution da…
Finite-Window Recursive Audit Chains for Navier-Stokes Generated Packages
Runlong Yu
We develop a finite-window recursive audit framework for Navier--Stokes-generated packages. On a fixed window, the underlying anti-phantom certificate asserts that a baseline-visib…
Finite-Window Local-to-Clean Transfer and Anti-Phantom Detection for Sharp Navier-Stokes Packages
Runlong Yu
We prove a fixed finite-window structural theorem for sharp localized Navier-Stokes packages, formulated as both a local-to-clean detection theorem and an anti-phantom principle. T…
Tail Criteria, No-Go Audits, and Apéry-Type Certificate Obstructions for the Irrationality of e+π
Runlong Yu
The irrationality of e+pi remains open, despite the separate transcendence of e and pi. This paper studies the problem from the viewpoint of finite irrationality certificates and g…
Finite-Window Computational Anti-Phantom Theorems for Scale-Critical Navier-Stokes Defects
Runlong Yu
We prove a finite-window anti-phantom principle for scale-critical Navier--Stokes defect packages and develop a conditional localized transfer framework around it. In a fixed clean…
Finite-Window Singularity Audits and Local-to-Clean Defect Transfer for Navier-Stokes
Runlong Yu
We develop a finite-window audit and transfer framework for the local regularity problem of the three-dimensional incompressible Navier--Stokes equations. The paper has two logical…
Critical Ledgers and Scale-Defect Cascades for Navier-Stokes
Runlong Yu
We prove a finite-scale supply--tax reduction for suitable weak solutions of the three-dimensional incompressible Navier--Stokes equations near the local regularity threshold. Alon…
Invisible Defect Cascades for Navier-Stokes Regularity
Runlong Yu
We formulate a conditional scale-critical defect-cascade reduction for the local regularity problem of the three-dimensional incompressible Navier--Stokes equations. The theorem co…
Schur Visibility and Anti-Phantom Reduction in One-Component Navier-Stokes Degeneration
Runlong Yu
We study the finite-scale one-component degeneration problem for suitable weak solutions of the three-dimensional incompressible Navier--Stokes equations under a scale-invariant bo…
Strict 2.5D Shadows for One-Component Navier-Stokes Regularity
Runlong Yu
We formulate and prove a conditional finite-scale reduction theorem for the local one-component regularity problem for suitable weak solutions of the three-dimensional Navier--Stok…
Finite-Scale One-Component Regularity via Harmonic Pressure for the 3D Navier-Stokes Equations
Runlong Yu
We study a finite-scale one-component regularity mechanism for suitable weak solutions of the three-dimensional incompressible Navier--Stokes equations. The results are organized i…