Pullback V-Attractors of the Stochastic Calmed 3D Navier-Stokes Equations

2025/09/28 by Duan, Yawen, Gu, Anhui
#35B40 #35B41 #35Q35 #37L55 #60H15 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2509.23553

Abstract

In this paper, we investigate a calmed version of the 3D rotational Navier-Stokes equations driven by additive noise. First, we use the Ornstein-Uhlenbeck process to transform the equation into a random one. By using the Galerkin approximation, we establish the global well-posedness of solutions for the calmed system. Then, we demonstrate the existence of a closed, measurable D_V-pullback absorbing set. Finally, by proving the pullback flattening property, we obtain the existence of a D_V-pullback attractor in \(V\).

Citations

• Calmed Ohmic Heating for the 2D Magnetohydrodynamic-Boussinesq System: Global Well-posedness and Convergence
• Calmed 3D Navier-Stokes Equations: Global Well-Posedness, Energy Identities, Global Attractors, and Convergence
• Algebraic calming for the 2D Kuramoto-Sivashinsky equations
• Sufficient and Necessary Criteria for Existence of Pullback Attractors for Non-compact Random Dynamical Systems

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• Existence and upper semicontinuity of random pullback attractors for 2D and 3D non-autonomous stochastic convective Brinkman-Forchheimer equations on whole domain