Navier-Stokes-Inspired Global Liquidity-Flow and Systemic-Stress Modelling: A Nondimensional Macro-Financial Stress-Testing Framework

Abstract

This study develops a global Navier-Stokes-inspired macro-financial stress-testing framework for measuring systemic stress as a nondimensional flow-pressure-friction-shock-cycle-closure process rather than as a collection of isolated macro-financial indicators. The framework does not claim that financial liquidity is a physical fluid, does not solve the mathematical Navier-Stokes problem and does not establish a universal crisis-prediction law. Instead, it translates the structural logic of velocity, acceleration, pressure gradients, diffusion/friction, external forcing and closure into an empirically auditable economic analogue. The empirical architecture is organized around a 100-country annual panel for 2010-2024, yielding 1,500 country-year observations, supplemented by a World aggregate anchor, macro-regional aggregation, rolling validation windows, robustness layers, external-target validation, Monte Carlo uncertainty analysis and policy counterfactuals. Systemic stress is constructed from normalized stress-direction components and interpreted jointly with liquidity resilience. The central balance decomposes stress into liquidity velocity weakness, liquidity acceleration, macro-financial pressure gradients, liquidity friction/diffusion, stochastic shocks, Fourier GDP-cycle forcing and a restricted hidden-adjustment term epsilon(t). The closure equation is modelled through observable or proxy-observable state variables, including lagged closure, shadow-economy pressure, external transfers, geopolitical shock, fiscal buffers, foreign aid/support and economic inertia, preventing epsilon(t) from operating as an unrestricted residual plug. The results show stable weighting robustness, coherent closure signs, strong rolling one-year-ahead validation performance over 2017-2024, favorable benchmark comparison against ARIMA, VAR, GARCH and composite-index baselines, statistically coherent fixed-effects associations, plausible external-target validation, residual stability, robustness under perturbation and interpretable Monte Carlo and policy-counterfactual effects. The contribution is methodological and empirical: a transparent, reproducible and scientifically bounded stress-testing architecture for global liquidity-flow diagnostics and systemic-risk interpretation.