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arXiv · 2008.04760

Non-uniqueness in law for two-dimensional Navier-Stokes equations with diffusion weaker than a full Laplacian

Kazuo Yamazaki
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Abstract

We study the two-dimensional Navier-Stokes equations forced by random noise with a diffusive term generalized via a fractional Laplacian that has a positive exponent strictly less than one. Because intermittent jets are inherently three-dimensional, we instead adapt the theory of intermittent form of the two-dimensional stationary flows to the stochastic approach presented by Hofmanov$\acute{\mathrm{a}}$, Zhu $\&$ Zhu (2019, arXiv:1912.11841 [math.PR]) and prove its non-uniqueness in law.

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Kazuo Yamazaki. 2022-06-23. Non-uniqueness in law for two-dimensional Navier-Stokes equations with diffusion weaker than a full Laplacian. https://arxiv.org/abs/2008.04760

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