Semantic Scholar Open Access 2020 26 sitasi

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

K. 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

Mathematics

Penulis (1)

K. Yamazaki

Format Sitasi

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Yamazaki, K. (2020). Remarks on the non-uniqueness in law of the Navier–Stokes equations up to the J.-L. Lions’ exponent. https://doi.org/10.1016/j.spa.2022.01.016

Akses Cepat

Lihat di Sumber doi.org/10.1016/j.spa.2022.01.016

Informasi Jurnal

Tahun Terbit: 2020
Bahasa: en
Total Sitasi: 26×
Sumber Database: Semantic Scholar
DOI: 10.1016/j.spa.2022.01.016
Akses: Open Access ✓