TY - JOUR
T1 - Deterministic and stochastic 2D Navier-Stokes equations with anisotropic viscosity
AU - Liang, Siyu
AU - Zhang, Ping
AU - Zhu, Rongchan
N1 - Publisher Copyright:
© 2020 Elsevier Inc.
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 -