Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum

Zhong, Xin

doi:10.3934/cpaa.2021185

Cited by 9 publications

(2 citation statements)

References 24 publications

(26 reference statements)

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“…Very recently, Zhong [22] considered the existence and exponential decay of global strong solutions to the 3D initial boundary problem of incompressible magnetomicropolar system with vacuum. However, the global existence of strong solution to the 3D Cauchy problem of ( 1)-( 2) with vacuum is not addressed.…”

Section: Global Solvability To Incompressible Magneto-micropolar Syst...mentioning

confidence: 99%

Global solvability to the 3D incompressible magneto-micropolar system with vacuum

Liu

Zhou

Guo

2022

DCDS-B

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This paper deals with the Cauchy problem of 3D innhomogeneous incompressible magneto-micropolar system. We prove the global existence of strong solutions to this system, with initial data being of small norm but allowed to have vacuum and large oscillations. More precisely, we only require that the initial data <inline-formula><tex-math id="M1">\begin{document}$ (\rho_0, u_0, w_0, b_0) $\end{document}</tex-math></inline-formula> satisfying<disp-formula> <label/> <tex-math id="FE1"> \begin{document}$ \begin{align*} &\Big(\|\sqrt{\rho_0}u_0\|_{L^2}^2+\|\sqrt{\rho_0}w_0\|_{L^2}^2+\|b_0\|_{L^2}^2\Big)\times\Big(\mu_1\|\nabla u_0\|_{L^2}^2 +\mu_2\|\nabla w_0\|_{L^2}^2\nonumber\\ &\quad+(\mu_2+\lambda)\|{\rm div}w_0\|_{L^2}^2+\eta\|\nabla b_0\|_{L^2}^2 +\xi\|2w_0-\nabla\times u_0\|_{L^2}^2\Big) \end{align*} $\end{document} </tex-math></disp-formula>is suitably small, which extends the corresponding Cruz and Novais's result (Appl. Anal., 2020[<xref ref-type="bibr" rid="b9">9</xref>]) to the inhomogeneous case, and Ye's result (Discrete Contin. Dyn. Syst. B, 2019[<xref ref-type="bibr" rid="b17">17</xref>]) to the 3D Cauchy problem of the inhomogeneous micropolar equations with magnetic field. Furthermore, we also established the large time behavior of strong solutions.

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Section: Global Solvability To Incompressible Magneto-micropolar Syst...mentioning

confidence: 99%

Global solvability to the 3D incompressible magneto-micropolar system with vacuum

Liu

Zhou

Guo

2022

DCDS-B

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“…Recently, With the help of Weighted function and the duality principle of BMO space and Hardy space, Zhong [19] investigated the global well-posedness to nonhomogeneous magneto-micropolar fluid equations with zero density at infinity in R 2 . Furthermore, for the homogeneous Dirichlet boundary conditions of the velocity and micro-rotational velocity and Navier-slip boundary condition of the magnetic field, he proved the initial boundary value problem of 3D nonhomogeneous magneto-micropolar fluid equations in [20]. The above results are all the density-independent viscosity.…”

Section: Introductionmentioning

confidence: 96%

Global well-posedness and exponential decay of strong solutions for 2D nonhomogeneous Magneto-Micropolar equations with density-dependent viscosity

Liu

2023

Preprint

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We study an initial boundary value problem of 2D nonhomogeneous magneto-micropolar equations with density-dependent viscosity in smooth bounded domains. When the initial density can contain vacuum states, we prove that there is a unique global strong solution for the system under the assumption that initial velocity is suitably small. In particular, the initial data can be arbitrarily large except the gradient of velocity. Finally, we obtain the exponential decay rates of strong solutions by using the energy method. MSC(2010). 35Q35, 76D03.

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Global well-posedness for 2D nonhomogeneous asymmetric fluids with magnetic field and density-dependent viscosity

Zhou,

Tang

2024

Z. Angew. Math. Phys.

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Global well-posedness and exponential decay for 3D nonhomogeneous magneto-micropolar fluid equations with vacuum

Cited by 9 publications

References 24 publications

Global solvability to the 3D incompressible magneto-micropolar system with vacuum

Global solvability to the 3D incompressible magneto-micropolar system with vacuum

Global well-posedness and exponential decay of strong solutions for 2D nonhomogeneous Magneto-Micropolar equations with density-dependent viscosity

Global well-posedness for 2D nonhomogeneous asymmetric fluids with magnetic field and density-dependent viscosity

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