PULLBACK ATTRACTOR OF STOCHASTIC NAVIER-STOKES EQUATIONS WITH RANDOM DENSITY

Phạm Trí Nguyễn

doi:10.34238/tnu-jst.11859

PULLBACK ATTRACTOR OF STOCHASTIC NAVIER-STOKES EQUATIONS WITH RANDOM DENSITY

About this article

Received: 10/01/25 Revised: 17/02/25 Published: 19/02/25

Authors

Pham Tri Nguyen , Electric Power University

Abstract

This paper studies the two dimensional Navier Stokes equations driven by random density, additive white noise and time dependent forces on bounded domain. The result shows that when the noise is zero and the random density is identical to one, the system becomes the classical incompressible Navier Stokes equation system. In addition, for the bounded domain, the Poincaré inequality is satisfied. By applying the Ornstein Uhlenbeck process, the stochastic system is transformed into a deterministic one with random parameters. Then, using the Faedo Galerkin approximations method we obtain the existence and unique weak solution for the system as well as the continuity of the solution with respect to its initial data. Next, a continuous cocycle for the equations is defined, the existence and unique pullback attractor of the system is proven. Noteworthy, for bounded domains, the use of the Sobolev embedding theorem helps to obtain the asymptotic compactness of the solution.

Keywords

Stochastic Navier-Stokes equations; Pullback attractor; Random density; Bounded domain; Additive noise

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DOI: https://doi.org/10.34238/tnu-jst.11859

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