On Asymptotic Stability of the 3D Boussinesq Equations with a Velocity Damping Term

Li-hua, Dong

doi:10.1007/s00021-022-00660-z

Cited by 6 publications

(3 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Comparing this result with theorem 1.1, we can improve the functional setting of the initial data for 2D. (b) When we were almost of the end of the first draft of this manuscript, we found the wellposedness and the asymptotic stability of (1.3) has been studied in the reference [10] (also see [11,12] for the full dissipation). In [10], Dong showed the asymptotic stability of (1.3) in R 3 by considering the vorticity equations.…”

Section: Remark 13mentioning

confidence: 67%

“…(b) When we were almost of the end of the first draft of this manuscript, we found the wellposedness and the asymptotic stability of (1.3) has been studied in the reference [10] (also see [11,12] for the full dissipation). In [10], Dong showed the asymptotic stability of (1.3) in R 3 by considering the vorticity equations. It is also assumed that (ω 0 , 4 , where m 32 and 0 < s < 1.…”

Section: Remark 13mentioning

confidence: 95%

“…It is also assumed that (ω 0 , 4 , where m 32 and 0 < s < 1. We emphasize the initial conditions in theorem 1.1 are more relaxed than the assumptions in [10].…”

Section: Remark 13mentioning

confidence: 99%

See 2 more Smart Citations

Stratified Boussinesq equations with a velocity damping term

Kim

Lee

2022

Nonlinearity

View full text Add to dashboard Cite

We consider an initial value problem of the multi-dimensional Boussinesq equations with velocity damping for strongly stratified fluids. We prove the global-in-time existence of the classical solution to the stratified damped Boussinesq equations with initial data near the stationary stratified solution ( v s , ρ s , p s ) = ( 0 , … , 0 , x d , x d 2 / 2 ) . We also show the asymptotic stability of the solutions near the stratified solution and obtain the temporal decay for the fluid velocity and the temperature by providing estimates for the Green function associated with the linear operator in any dimension.

show abstract

Section: Remark 13mentioning

confidence: 67%

Section: Remark 13mentioning

confidence: 95%

See 1 more Smart Citation

Stratified Boussinesq equations with a velocity damping term

Kim

Lee

2022

Nonlinearity

View full text Add to dashboard Cite

show abstract

Stability and optimal decay estimates for the 3D anisotropic Boussinesq equations

Yang,

Peng

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

This paper focuses on the three‐dimensional (3D) incompressible anisotropic Boussinesq system while the velocity of fluid only involves horizontal dissipation and the temperature has a damping term. By utilizing the structure of the system, the energy methods and the means of bootstrapping argument, we prove the global stability property in the Sobolev space of perturbations near the hydrostatic equilibrium. Moreover, we take an effective approach to obtain the optimal decay rates for the global solution itself as well as its derivatives. In this paper, we aim to reveal the mechanism of how the temperature helps stabilize the fluid. Additionally, exploring the stability of perturbations near hydrostatic equilibrium may provide valuable insights into specific severe weather phenomena.

show abstract

Stability of the 2D Boussinesq equations with a velocity damping term in the strip domain

Luo

Ren

2023

Z. Angew. Math. Phys.

View full text Add to dashboard Cite

On Asymptotic Stability of the 3D Boussinesq Equations with a Velocity Damping Term

Cited by 6 publications

References 20 publications

Stratified Boussinesq equations with a velocity damping term

Stratified Boussinesq equations with a velocity damping term

Stability and optimal decay estimates for the 3D anisotropic Boussinesq equations

Stability of the 2D Boussinesq equations with a velocity damping term in the strip domain

Contact Info

Product

Resources

About