Large Time Decay for the Magnetohydrodynamics System in $\dot{\boldsymbol{H}^{s}}(\mathbb{R}^{n})$
Sign Up to like & getrecommendations! Published in 2019 at "Acta Applicandae Mathematicae"
DOI: 10.1007/s10440-019-00276-y
Abstract: We show that $t^{s/2} \| (\boldsymbol{u},\boldsymbol{b})(t) \|_{{\dot{H}^{s}(\mathbb{R}^{n})}} \to0 $ as $t \to\infty$ for global Leray solutions $(\boldsymbol{u},\boldsymbol{b})(t)$ of the incompressible MHD equations, where $2 \leq n \leq4$ and $s \geq0$ (real). We also provide some… read more here.
Keywords: large time; boldsymbol; magnetohydrodynamics; time decay ... See more keywords
Global well-posedness and time-decay estimates for compressible Navier-Stokes equations with reaction diffusion
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DOI: 10.1007/s11425-020-1779-7
Abstract: We consider the full compressible Navier-Stokes equations with reaction diffusion. A global existence and uniqueness result of the strong solution is established for the Cauchy problem when the initial data is in a neighborhood of… read more here.
Keywords: compressible navier; stokes equations; time; time decay ... See more keywords
Time decay rate of global strong solutions to nematic liquid crystal flows in R+3
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DOI: 10.1016/j.jde.2019.02.021
Abstract: In this paper, we obtain optimal time-decay rates in $L^r(\mathbb R^3_+)$ for $r\ge 1$ of global strong solutions to the nematic liquid crystal flows in $\mathbb R^3_+$, provided the initial data has small $L^3(\mathbb R^3_+)$-norm. read more here.
Keywords: nematic liquid; global strong; time decay; liquid crystal ... See more keywords
Optimal time-decay estimates for an Oldroyd-B model with zero viscosity
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DOI: 10.1016/j.jde.2021.10.046
Abstract: In this work, we consider the Cauchy problem for a diffusive Oldroyd-B model in three dimensions. Some optimal time-decay rates of the solutions are derived via analysis of upper and lower time-decay estimates provided that… read more here.
Keywords: oldroyd model; time; optimal time; time decay ... See more keywords
Large Time Decay Rates of the 2D Micropolar Equations with Linear Velocity Damping
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DOI: 10.3390/math11102311
Abstract: 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… read more here.
Keywords: equations linear; time; decay rates; time decay ... See more keywords
Global large solutions and optimal time-decay estimates to the Korteweg system
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DOI: 10.3934/dcds.2020322
Abstract: We prove the global solutions to the Korteweg system without smallness condition imposed on the vertical component of the incompressible part of the velocity. The weighted Chemin-Lerner-norm technique which is well-known for the incompressible Navier-Stokes… read more here.
Keywords: korteweg system; time decay; system; optimal time ... See more keywords