Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity

Siyu Liang; Ping Zhang; Rongchan Zhu

doi:10.1016/j.jde.2020.11.028

Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity

Siyu Liang, Ping Zhang, Rongchan Zhu^*

^*Corresponding author for this work

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

7 Citations (Scopus)

Abstract

In this paper, we investigate both deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev space H˜^0,1. For the stochastic case, we obtain existence of the martingale solutions and pathwise uniqueness of the solutions, which imply existence of the probabilistically strong solution to this system by the Yamada-Watanabe Theorem.

Original language	English
Pages (from-to)	473-508
Number of pages	36
Journal	Journal of Differential Equations
Volume	275
DOIs	https://doi.org/10.1016/j.jde.2020.11.028
Publication status	Published - 25 Feb 2021

Access to Document

10.1016/j.jde.2020.11.028

Cite this

Liang, S., Zhang, P., & Zhu, R. (2021). Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. Journal of Differential Equations, 275, 473-508. https://doi.org/10.1016/j.jde.2020.11.028

@article{dda4fe1f13964f2885c34666aba2bcb5,

title = "Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity",

abstract = "In this paper, we investigate both deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev space H˜0,1. For the stochastic case, we obtain existence of the martingale solutions and pathwise uniqueness of the solutions, which imply existence of the probabilistically strong solution to this system by the Yamada-Watanabe Theorem.",

author = "Siyu Liang and Ping Zhang and Rongchan Zhu",

note = "Publisher Copyright: {\textcopyright} 2020 Elsevier Inc.",

year = "2021",

month = feb,

day = "25",

doi = "10.1016/j.jde.2020.11.028",

language = "English",

volume = "275",

pages = "473--508",

journal = "Journal of Differential Equations",

issn = "0022-0396",

publisher = "Academic Press Inc.",

}

TY - JOUR

T1 - Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity

AU - Liang, Siyu

AU - Zhang, Ping

AU - Zhu, Rongchan

PY - 2021/2/25

Y1 - 2021/2/25

N2 - In this paper, we investigate both deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev space H˜0,1. For the stochastic case, we obtain existence of the martingale solutions and pathwise uniqueness of the solutions, which imply existence of the probabilistically strong solution to this system by the Yamada-Watanabe Theorem.

AB - In this paper, we investigate both deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity. For the deterministic case, we prove the global well-posedness of the system with initial data in the anisotropic Sobolev space H˜0,1. For the stochastic case, we obtain existence of the martingale solutions and pathwise uniqueness of the solutions, which imply existence of the probabilistically strong solution to this system by the Yamada-Watanabe Theorem.

UR - http://www.scopus.com/inward/record.url?scp=85096880714&partnerID=8YFLogxK

U2 - 10.1016/j.jde.2020.11.028

DO - 10.1016/j.jde.2020.11.028

M3 - Article

AN - SCOPUS:85096880714

SN - 0022-0396

VL - 275

SP - 473

EP - 508

JO - Journal of Differential Equations

JF - Journal of Differential Equations

ER -

Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity

Abstract

Access to Document

Other files and links

Fingerprint

Cite this