Quantum-Inspired Stochastic Modeling and Regularity in Turbulent Fluid Dynamics

TL;DR

This paper introduces a quantum-inspired stochastic framework for analyzing turbulence in fluid dynamics, combining advanced mathematical spaces with quantum effects to improve understanding of energy transfer and flow regularity.

Contribution

It develops novel regularity theorems and anisotropic stochastic models incorporating quantum-inspired operators for better turbulence representation.

Findings

New regularity theorems for stochastic Navier-Stokes equations

Quantum-inspired Schrödinger-like operator captures turbulence effects

Anisotropic models improve real-world flow simulations

Abstract

This paper presents an innovative framework for analyzing the regularity of solutions to the stochastic Navier-Stokes equations by integrating Sobolev-Besov hybrid spaces with fractional operators and quantum-inspired dynamics. We propose new regularity theorems that address the multiscale and chaotic nature of fluid flows, offering novel insights into energy dissipation mechanisms. The introduction of a Schr\"odinger-like operator into the fluid dynamics model captures quantum-scale turbulence effects, enhancing our understanding of energy redistribution across different scales. The results also include the development of anisotropic stochastic models that account for direction-dependent viscosity, improving the representation of real-world turbulent flows. These advances in stochastic modeling and regularity analysis provide a comprehensive toolset for tackling complex fluid dynamics problems. The findings are applicable to fields such as engineering, quantum turbulence, and environmental sciences. Future directions include the numerical implementation of the proposed models and the use of machine learning techniques to optimize parameters for enhanced simulation accuracy.