Increasing Systemic Resilience to Socioeconomic Challenges: Modeling the Dynamics of Liquidity Flows and Systemic Risks Using Navier–Stokes Equations

Modern economic systems face unprecedented socioeconomic challenges, which make increasing systemic resilience and improving liquidity flow management particularly important. Traditional models (CAPM, VaR, GARCH) often fail to reflect real market fluctuations and extreme events. In the presented study, an innovative mathematical model has been developed, which is based on the interpretation of the Navier-Stokes equations and aims at the quantitative assessment, forecasting, and simulation analysis of liquidity flows and systemic risks. The main hypothesis of the study is that the adapted form of the Navier-Stokes equations in financial modeling allows us to accurately study the internal dynamics of the market, liquidity diffusion, the impact of external shocks, and structural tensions. The model integrates 13 macroeconomic and financial parameters, including liquidity velocity, market pressure, internal stress, beta coefficient, stochastic fluctuations, risk premiums, and contingency factors, all based on real statistical data and formally incorporated into the modified equation. The methodology is based on a mixed approach: econometric testing, Fourier analysis, stochastic simulations, and AI-algorithm tuning, which together provide dynamic testing, calibration, and forecasting capabilities of the model. Simulation-based sensitivity analysis is used, which assesses the impact of parameter changes on the financial balance. The proposed model is empirically validated using macroeconomic and financial data from Georgia for the period 2010–2024. The model is validated using empirical data such as Gross Domestic Product (GDP), inflation, the Gini index, Credit Default Swap (CDS) spreads, and Liquidity Coverage Ratio (LCR) metrics.The results indicate that the model effectively describes the dynamics of liquidity, systemic risks and extreme financial scenarios. The balancing of the model’s equations' left and right sides is conducted under real and simulated conditions. When discrepancies occur, a dynamic balance term, represented as a time-varying residual force, ensures systemic adaptation. In addition, the cyclical components obtained by Fourier analysis are harmoniously related to economic cycles and increase the accuracy of the model's predictions. The scientific significance of the study lies in the fact that it creates a mathematically balanced framework for a multifactorial analysis of the behavior of the financial system, which makes it possible not only to predict crises, but also to plan countercyclical policies and increase systemic stability. This model represents a significant scientific advance in the field of economic modeling and creates a real opportunity to increase the resilience of financial systems to socioeconomic fluctuations and systemic risks.