arXiv Open Access 2020

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

Kazuo Yamazaki

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Abstrak

Lions (1959, Bull. Soc. Math. France, \textbf{87}, 245--273) 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 Hofmanov$\acute{\mathrm{a}}$, Zhu and Zhu (2019, arXiv:1912.11841 [math.PR]), 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.

Topik & Kata Kunci

math.AP

Penulis (1)

Kazuo Yamazaki

Format Sitasi

APA MLA BibTeX

Yamazaki, K. (2020). Remarks on the non-uniqueness in law of the Navier-Stokes equations up to the J.-L. Lions' exponent. https://arxiv.org/abs/2006.11861

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Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Sumber Database: arXiv
Akses: Open Access ✓