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

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.

arXiv admin note: text overlap with arXiv:2006.11861. This is the version that was accepted by SIAM Journal on Mathematical Analysis (SIMA), before the final edit by the journal

Cited by in corpus (1)

• Non-uniqueness in law for Boussinesq system forced by random noise