TẬP HÚT LÙI CỦA HỆ NAVIER-STOKES NGẪU NHIÊN VỚI NHIỄU NHÂN TÍNH VÀ MẬT ĐỘ NGẪU NHIÊN
Main Article Content
Abstract
Trong bài báo này, chúng tôi xét hệ phương trình Navier-Stokes hai chiều với nhiễu nhân tính và mật độ ngẫu nhiên. Sử dụng phép đổi biến thích hợp, chúng tôi chuyển hệ ngẫu nhiên thành hệ tất định với các tham số ngẫu nhiên, từ đó chúng tôi chứng minh sự tồn tại và duy nhất tập hút lùi của hệ.
Keywords
Tập hút lùi, Hệ Navier-Stokes ngẫu nhiên, Nhiễu nhân tính, Mật độ ngẫu nhiên.
Article Details
References
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[4] B. Gess, W. Liu, M. Rockner, Random attractors for a class of stochastic partial differential equations driven by general additive noise, J. Differential Equations 251 pp. 1225-1253, 2011.
[5] A. Gu, K. Lu, B. Wang, Asymptotic behavior of random Navier-Stokes equations driven by Wong-Zakai approximations, Discrete and Continuous Dynamical Systems 39 (1) pp. 185-218, 2019.
[6] J. C. Robinson, Infinite-Dimensional Dynamical Systems: An Introduction
to Dissipative Parabolic PDEs and the Theory of Global Attractors, Cambridge Texts in Applied Mathematics, Series Number 28, 2001.
[7] R. Temam, Infnite-Dimensional Dynamical Systems in Mechanics and Physics, Springer-Verlag, New York, 1997.
[8] B. Wang, Random attractors for non-autonomous stochastic wave equations with multiplicative noise, Discrete and Continuous Dynamical Systems 34 (1) pp. 269-300, 2014.
[9] B. Wang, Periodic random attractors for stochastic Navier-Stokes equations on unbounded domains, Electronic Journal of Differential Equations, vol. 2012, no. 59, pp. 1-18, 2012.