A stochastic Lagrangian representation of the three‐dimensional incompressible Navier‐Stokes equations
By Peter Constantin, Gautam Iyer. 2005
195 citations recorded by the source corpus.
In this paper we derive a probabilistic representation of the deterministic three‐dimensional Navier‐Stokes equations based on stochastic Lagrangian paths. The particle trajectories obey SDEs driven by a uniform Wiener process; the inviscid Weber formula for the Euler equations of ideal fluids is used to recover the velocity field. This method admits a self‐contained proof of local existence for the nonlinear stochastic system and can be extended to formulate stochastic representations of related hydrodynamic‐type equations, including viscous Burgers equations and Lagrangian‐averaged Navier‐Stokes alpha models. © 2007 Wiley Periodicals, Inc.
Subfields: Applied Mathematics, Computational Mechanics, Finance
View Paper: https://www.semanticscholar.org/paper/cdd6b5bbe9327569da2e052317b906895e97e82a
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In Applied Mathematics
In Computational Mechanics
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Citations in the corpus
- Fluid flow dynamics under location uncertainty (2013, methodology): “This framework is also related to the work of Constantin and Iyer (2008).”
- Ltd Registered in England and Wales Registered Number : 1072954 Registered office : (2004, methodology): “For example, in the work of Constantin and Iyer [9], the drift term in the stochastic differential equation is computed implicitly as the expected value of an expression involving the flow it drives.”
- Stochastic differential equations with Sobolev diffusion and singular drift and applications (2016, unknown): “In [1], Constantin and Iyer provided a probabilistic representation to the above NSE as follows: ⎧⎪⎨ ⎪⎩ Xt(x) = x + ∫ t”