Quantum-Inspired Stochastic Modeling and Regularity Analysis in Turbulent Flows

Rômulo Damasclin Chaves dos Santos; Jorge Henrique de Oliveira Sales

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arXiv · 2411.09888

Quantum-Inspired Stochastic Modeling and Regularity Analysis in Turbulent Flows

Rômulo Damasclin Chaves dos Santos·Jorge Henrique de Oliveira Sales

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Abstract

This paper introduces a novel mathematical framework for examining the regularity and energy dissipation properties of solutions to the stochastic Navier-Stokes equations. By integrating Sobolev-Besov hybrid spaces, fractional differential operators, and quantum-inspired modeling techniques, we provide a comprehensive analysis that captures the multiscale and chaotic dynamics inherent in turbulent flows. Central to this framework is a Schr\"odinger-type operator adapted for fluid dynamics, which encapsulates quantum-scale turbulence effects, thereby elucidating the mechanisms of energy redistribution across scales. Additionally, we develop anisotropic stochastic models with direction-dependent viscosity, characterized by a pseudo-differential operator and a covariance matrix governing directional diffusion. These models more accurately reflect real-world turbulence, where viscosity varies with flow orientation, enhancing both theoretical insights and practical simulation capabilities. Our main contributions include new regularity theorems and rigorous a priori estimates for solutions in Sobolev-Besov spaces, alongside proofs of energy dissipation properties in anisotropic contexts. These findings advance the understanding of fluid turbulence by offering a refined approach to studying scale interactions, stochastic effects, and anisotropy in turbulent flows.

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Rômulo Damasclin Chaves dos Santos, Jorge Henrique de Oliveira Sales. 2024-11-15. Quantum-Inspired Stochastic Modeling and Regularity Analysis in Turbulent Flows. https://arxiv.org/abs/2411.09888

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