Euler-Navier-Stokes Regularity Suite: Numerical Artifacts, Structural Instability, and Computer-Assisted Proofs (Volumes I–III & Verification Suite)

This record archives the complete three-volume research suite and open-source verification framework establishing the structural instability, nonlocal pressure barriers, and generic regularity of boundary-driven Euler and Navier–Stokes flows: • Volume I (01_Euler_Singularity_Numerical_Artifacts_and_Pressure_Barriers.pdf):Investigates the 2D Boussinesq boundary model via differentiable Lagrangian inverse design. Identifies that apparent finite-time blowup (γ ≈ 1.59) and dissipative bifurcations (Re_c ≈ 26.5) under iterative Jacobi solvers stem from unresolved vortex core collapse (N_core < 2) and Poisson pressure leakage (residual factor 1.01 × 10¹²). Proves that machine-precision spectral DST-I projection restores nonlocal pressure repulsion and Kelvin–Helmholtz roll-up, saturating peak vorticity. • Volume II (02_Euler_Structural_Instability_and_Generic_Regularity.pdf):Examines boundary-driven flows when corner pinning and mirror reflectional symmetries are relaxed. Shows that non-smooth C^(1,α) corner profiles trigger advective sweep-out (saturating at ||ω|| ≤ 76.1), while active boundary shear layers undergo spontaneous Kelvin–Helmholtz wall detachment (x_core: 0.04 → 0.86), converting 1D compressive strain into 2D dipole rotation. • Volume III (03_Euler_Spectral_Instability_and_Measure_Zero_CAP.pdf):Formulates a mathematically certified Computer-Assisted Proof (CAP) via interval arithmetic and the Newton–Kantorovich contraction theorem (h = 7.61 × 10⁻⁹ ≪ 0.5). Encloses the true leading eigenvalue within B(λ_0, r*) with Re(λ_u*) ≥ +6.4382 > 0, proving the stable blowup manifold has codimension ≥ 1 (measure zero / shy set). Establishes a two-sided sandwich regularity bound for the 3D Navier–Stokes equations. • Verification Suite (Euler_NavierStokes_Suite_Codes.zip):Complete, fully reproducible Python/PyTorch codebase (Parts 1–3, Modules 01 through 11) containing GPU-accelerated spectral solvers, automatic differentiation scripts, multi-grid audits, and interval eigenvalue certification tools. • GitHub Repository (Open-Source Verification Suite):https://github.com/CitizenKorea/euler-navier-stokes-regularity-suite