The decay and stability of solutions for the 3D density-dependent incompressible Boussinesq system

2021/09/06 by Liu, Xiaopan, Zhang, Qingshan
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2109.02268

Abstract

This paper deals with stability and the large-time decay to any given global smooth solutions of the 3D density-dependent incompressible Boussinesq system. The decay rate for solutions of the corresponding Cauchy problem is obtained in this work. With the aid of this decay rate, it is shown that a small perturbation of initial data (a₀,θ₀, u₀) still generates a global smooth solution to the density-dependent Boussinesq system, and this solution keeps close to the reference solution.

Related

• On Asymptotic Properties of the Boussinesq Equations
• Derivation of limit equation for a perturbed 3D periodic Boussinesq system
• Linear and nonlinear stability for the 3D stratified Boussinesq equations with the horizontal viscosity and diffusivity
• Existence of one class of global strong solution to the Cauchy problem for the three-dimensional incompressible Boussinesq system
• Global well-posedness and exponential decay of strong solution to the three-dimensional nonhomogeneous Bénard system with density-dependent viscosity and vacuum