The Navier-Stokes-$\alpha$ equation via forward-backward stochastic differential systems

Guoping Liu

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arXiv · 1610.09421

The Navier-Stokes-$\alpha$ equation via forward-backward stochastic differential systems

Guoping Liu

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Abstract

In this paper, we use forward-backward stochastic differential systems to study the solution of two and d dimensional ($d\geq 3$) Navier-Stokes-$\alpha$ equation. For the two dimensional Navier-Stokes-$\alpha$ equation with space periodic boundary conditions, we derive the Feynmann-Kac formula associated with the vorticity equation and prove the global existence and uniqueness of the solution. For the d dimensional ($d\geq 3$) case, we prove the local existence and uniqueness of the solution in Sobolev space.

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Guoping Liu. 2016-10-28. The Navier-Stokes-$\alpha$ equation via forward-backward stochastic differential systems. https://arxiv.org/abs/1610.09421

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