Remarks on the non-uniqueness in law of the Navier–Stokes equations up to the J.-L. Lions’ exponent

Kazuo Yamazaki

Stochastic Processes and their Applications, 2022, vol. 147, issue C, 226-269

Abstract: Lions (1959), introduced the Navier–Stokes equations with a viscous diffusion in the form of a fractional Laplacian; subsequently, he (1969, Dunod, Gauthiers-Villars, Paris) claimed the uniqueness of its solution when its exponent is not less than five quarters in case the spatial dimension is three. Following the work of Hofmanová et al. (2019), we prove the non-uniqueness in law for the three-dimensional stochastic Navier–Stokes equations with the viscous diffusion in the form of a fractional Laplacian with its exponent less than five quarters.

Keywords: Convex integration; Fractional Laplacian; Navier–Stokes equations; Non-uniqueness; Random noise (search for similar items in EconPapers)
Date: 2022
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DOI: 10.1016/j.spa.2022.01.016

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