Existence of random attractors and the upper semicontinuity for small random perturbations of 2D Navier-Stokes equations with linear damping-Reference-Cited by-同舟云学术

Existence of random attractors and the upper semicontinuity for small random perturbations of 2D Navier-Stokes equations with linear damping

Published:2021-01-01 Issue:1 Volume:19 Page:1528-1537
ISSN:2391-5455
Container-title:Open Mathematics
language:en
Short-container-title:

Author:

Li Haiyan¹,Wang Bo²

Affiliation:

1. School of Mathematics and Information Science, North Minzu University, Yinchuan , Ningxia 750021 , P.R. China

2. School of Business, North Minzu University, Yinchuan , Ningxia 750021 , P.R. China

Abstract

Abstract The incompressible 2D stochastic Navier-Stokes equations with linear damping are considered in this paper. Based on some new calculation estimates, we obtain the existence of random attractor and the upper semicontinuity of the random attractors as

ε → 0 +

\varepsilon \to {0}^{+}

on the two-dimensional space.

Publisher

Walter de Gruyter GmbH

Subject

General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/math-2021-0098/pdf

Reference14 articles.

1. A. A. Ilyin , A. Miranville , and E. S. Titi , Small viscosity sharp estimates for the global attractor of the 2-D damped-driven Navier-Stokes equations, Commun. Math. Sci. 2 (2004), no. 3, 403–426, https://dx.doi.org/10.4310/CMS.2004.v2.n3.a4 .

2. A. A. Ilyin and E. S. Titi , Sharp estimates for the number of degrees of freedom for the damped-driven 2-D Navier-Stokes equations, J. Nonlinear Sci. 16 (2006), 233–253, https://doi.org/10.1007/s00332-005-0720-7.

3. P. Constantin and F. Ramos , Inviscid limit for damped and driven incompressible Navier-Stokes equations in R2 , Commun. Math. Phys. 275 (2007), no. 2, 529–551, https://doi.org/10.1007/s00220-007-0310-7.

4. R. Rosa , The global attractor for the 2D Navier-Stokes flow on some unbounded domains, Nonlinear Anal. 32 (1998), no. 1, 71–85, https://doi.org/10.1016/S0362-546X(97)00453-7 .

5. W. Zhao and Z. Zheng , On the incompressible Navier-Stokes equations with damping, Appl. Math. 4 (2013), no. 4, 652–658, http://dx.doi.org/10.4236/am.2013.44089.