Malliavin calculus for the stochastic 2D Navier—Stokes equation
Malliavin calculus for the stochastic 2D Navier—Stokes equation
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随机二维纳维-斯托克斯方程的 Malliavin 微积分
DOI：
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发表时间：
2004
期刊：
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通讯作者：
É. Pardoux
中科院分区：
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作者：
Jonathan C. Mattingly;É. Pardoux
考虑在时间白化的随机强迫作用下，二维不可压缩的N-S方程的周期边界条件。在有限维解的任意有限维投影关于勒贝格测度具有光滑的严格正密度的条件下，证明了解的几何约束条件是有限维的。特别是，我们的条件是粘度无关的。我们主要对激发极少数模式的强迫感兴趣。所有结果都依赖于证明无限维Malliavin矩阵的非退化性质。©2006威利期刊公司。
We consider the incompressible, two‐dimensional Navier‐Stokes equation with periodic boundary conditions under the effect of an additive, white‐in‐time, stochastic forcing. Under mild restrictions on the geometry of the scales forced, we show that any finite‐dimensional projection of the solution possesses a smooth, strictly positive density with respect to Lebesgue measure. In particular, our conditions are viscosity independent. We are mainly interested in forcing that excites a very small number of modes. All of the results rely on proving the nondegeneracy of the infinite‐dimensional Malliavin matrix. © 2006 Wiley Periodicals Inc.