Time decay rate of solutions to the hyperbolic mhd equations in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" overflow="scroll"><mml:mrow><mml:msup><mml:mi>ℝ</mml:mi><mml:mn>3</mml:mn></mml:msup></mml:mrow></mml:math>

Li, Bei; Zhu, Hongjin; Zhao, Caidi

doi:10.1016/s0252-9602(16)30075-3

Cited by 9 publications

(5 citation statements)

References 24 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…When ω = 0 , the micropolar Equation (1) reduces to the classic Navier-Stokes equations [7][8][9]. Because these equations are mathematically significant, the well-posedness and large time behavior of the micropolar equations attract considerable attention.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Large Time Decay Rates of the 2D Micropolar Equations with Linear Velocity Damping

Wu,

Wang,

Zou

2023

Mathematics

View full text Add to dashboard Cite

This paper studies the large time behavior of solutions to the 2D micropolar equations with linear damping velocity. It is proven that the global solutions have rapid time decay rates ∥∇ω∥L2+∥∇u∥L2≤C(1+t)−32 and ∥u∥L2≤C(1+t)−32,∥ω∥L2≤C(1+t)−1. The findings are mainly based on the new observation that linear damping actually improves the low-frequency effect of the system. The methods here are also available for complex fluid models with linear damping structures.

show abstract

Section: Introduction and Main Resultsmentioning

confidence: 99%

Large Time Decay Rates of the 2D Micropolar Equations with Linear Velocity Damping

Wu,

Wang,

Zou

2023

Mathematics

View full text Add to dashboard Cite

show abstract

“…ν > 0 and κ > 0 denote the viscosity and the magnetic resistivity respectively. The length scale α is a characterizing parameter of the elasticity of the fluid in the sense that α 2 ν is a characteristic relaxation time scale of the viscoelastic material [12]. In the case α = 0, the system (1.1) is called the standard MHD equations.…”

mentioning

confidence: 99%

“…The Voigt-regularization of 3D MHD equations has been studied in [4,9,10,12], which is critical to understanding a wide range of astrophysical and laboratory phenomena, and making it a cornerstone of MHD research. In [10], TiTi and Larios have proved the existence, uniqueness and higher-order global regularity of strong solution to a particular 3D inviscid resistive MHD-Voigt equations.…”

mentioning

confidence: 99%

“…In this article, we use the Fourier splitting method to prove decay rate, which has been built by Schonbek in [17,18]. Subsequently, the Fourier splitting method was significantly extended to explore the decay behavior of PDE in mathematical physics in [12]. In [24], Zhao and Zhu employed this method to establish the L 2 decay rate of weak solutions for the Navier-Stokes equations with the Voigt term and yielded the following result:…”

mentioning

confidence: 99%

See 1 more Smart Citation

Uniqueness and time decay rate of weak solution to the 3D Voigt-regularized magnetohydrodynamic equations

Zhang,

Yang

2024

DCDS-S

View full text Add to dashboard Cite

In this paper, the influence of the Voigt term −α∆ut on the wellposedness of the Magnetohydrodynamical (MHD) equations is considered. Especially, the L p estimate of the magnetic field is established by using the regularity of fluid velocity. Then, the uniqueness for weak solution of the 3D Voigt-regularized Magnetohydrodynamical model is obtained. Finally, the time decay rate for the weak solution of this MHD-Voigt equations is established by the Fourier splitting method.

show abstract

“…Schonbek and Wiegner [32], and references therein; for the MHD equations and related models, see Ahn [1], Chae and M.E. Schonbek [10], de Souza, Melo and Zingano [12], Duan, Fukumoto and Zhao [14], Li , Zhu and Zhao [21], Melo, Perusato, Guterres and Nunes [22], Weng [34], [35], Wu, Yu and Tang [36], Zhao [38], [40], [39], Zhao and Zhu [41], [42], [43] ; for families of dissipative equations, see Bae and Biswas [2], Biswas [4], Braz e Silva, Guterres, Perusato and P. Zingano [26], Niche and M.E. Schonbek [24]; and for many other equations.…”

mentioning

confidence: 99%

Upper and lower $\dot{H}^{m}$ estimates for solutions to parabolic equations

Guterres¹,

Niche²,

Perusato³

et al. 2022

Preprint

View full text Add to dashboard Cite

In this article we prove results concerning upper and lower decay estimates for homogeneous Sobolev norms of solutions to a rather general family of parabolic equations. Following the ideas of Kreiss, Hagstrom, Lorenz and Zingano, we use eventual regularity of solutions to directly work with smooth solutions in physical space, bootstrapping decay estimates from the L 2 norm to higher order derivatives. Besides obtaining upper and lower bounds through this method, we also obtain reverse results: from higher order derivatives decay estimates, we deduce bounds for the L 2 norm. We use these general results to prove new decay estimates for some equations and to recover some well known results.

show abstract

Time decay rate of solutions to the hyperbolic mhd equations inℝ3

Cited by 9 publications

References 24 publications

Large Time Decay Rates of the 2D Micropolar Equations with Linear Velocity Damping

Large Time Decay Rates of the 2D Micropolar Equations with Linear Velocity Damping

Uniqueness and time decay rate of weak solution to the 3D Voigt-regularized magnetohydrodynamic equations

Upper and lower $\dot{H}^{m}$ estimates for solutions to parabolic equations

Contact Info

Product

Resources

About