Large time decay properties of solutions to a viscous Boussinesq system in a half space

2013/09/17 by Peiran Han, P. Han, Han, P. +3
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP

paper · pdf · doi:10.48550/arxiv.1309.4505

arxiv created 2013/09/17 · openalex publication_date 2013/09/17 · arxiv updated 2013/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the long time behavior of weak and strong solutions of the n-dimensional viscous Boussinesq system in the half space, with n≥3 . The L^r(Rⁿ₊)-asymptotics of strong solutions and their first three derivatives, with 1≤ r≤∞, are derived combining L^q-L^r estimates and properties of the fractional powers of the Stokes operator. For the L^∞-asymptotics of the second order derivatives the unboundedness of the projection operator P: L^∞(Rⁿ₊)→ L^∞_σ(Rⁿ₊) is dealt by an appropriate decomposition of the nonlinear term.

Citations

• StrongL p -solutions of the Navier-Stokes equation inR m , with applications to weak solutions
• On the global well-posedness for Boussinesq system
• Global regularity for the 2D Boussinesq equations with partial viscosity terms

Related

• Optimal decay of global strong solutions to nematic liquid crystal flows in the half-space
• Large time behavior for the nonlinear dissipative Boussinesq equation
• On Asymptotic Properties of the Boussinesq Equations
• Characterization of solutions to dissipative systems with sharp algebraic decay
• The existence and space-time decay rates of strong solutions to Navier-Stokes Equations in weighed L^∞(|x|^γ\rm dx)∩ L^∞(|x|^β\rm dx) spaces