2021/03/03 by Kush Kinra, Kinra, Kush, Manil T. Mohan +1
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Stability and Controllability of Differential Equations
paper · pdf · doi:10.48550/arxiv.2103.02154
openalex publication_date 2021/03/03 · openalex created_date 2022/07/25 · openalex updated_date 2026/07/28
This work deals with the asymptotic behavior of the two as well as three dimensional convective Brinkman-Forchheimer (CBF) equations in periodic domains: \frac∂\boldsymbolu∂ t-μΔ\boldsymbolu+(\boldsymbolu⋅∇)\boldsymbolu+α\boldsymbolu+β|\boldsymbolu|r-1\boldsymbolu+∇ p=\boldsymbolf, ∇⋅\boldsymbolu=0, where r≥1. We prove that the global attractor of the above system is a singleton under small forcing intensity (r≥ 1 for n=2 and r≥ 3 for n=3 with 2βμ≥ 1 for r=n=3). After perturbing the above system with additive or multiplicative white noise, the random attractor does not have a singleton structure. But we obtain that the random attractor for 2D stochastic CBF equations with additive and multiplicative white noise converges towards the deterministic singleton attractor for 1≤ r≤ 2 and 1≤ r