Global strong solution and exponential decay for nonhomogeneous Navier-Stokes and magnetohydrodynamic equations

Zhong, Xin

doi:10.3934/dcdsb.2020246

Cited by 9 publications

(5 citation statements)

References 20 publications

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“…Moreover, they derived the global strong solution provided that the initial data satisfy some smallness condition. However, once we consider 2D problem of (), there is no need to require any additional smallness condition on the initial data for the global existence and uniqueness of strong solutions, as showed in Huang and Wang 8 (see also Zhong 9 ) and Lü et al 10 Recently, without using (), Song 11 and Lü et al 12 established the local strong solutions to the 3D and 2D Cauchy problem of () by time‐weighted estimates, respectively.…”

Section: Introduction and Main Resultsmentioning

confidence: 99%

Local well‐posedness to the 2D Cauchy problem of nonhomogeneous heat‐conducting Navier–Stokes and magnetohydrodynamic equations with vacuum at infinity

Chen

Zhong

2022

Math Methods in App Sciences

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This paper concerns the Cauchy problem of nonhomogeneous heat‐conducting magnetohydrodynamic (MHD) equations in ℝ2 with vacuum as far‐field density. By spatial weighted energy method, we derive the local existence and uniqueness of strong solutions provided that the initial density and the initial magnetic decay not too slowly at infinity. As a byproduct, we get the local existence of strong solutions to the 2D Cauchy problem for nonhomogeneous heat‐conducting Navier–Stokes equations with vacuum at infinity.

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Section: Introduction and Main Resultsmentioning

confidence: 99%

Local well‐posedness to the 2D Cauchy problem of nonhomogeneous heat‐conducting Navier–Stokes and magnetohydrodynamic equations with vacuum at infinity

Chen

Zhong

2022

Math Methods in App Sciences

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“…For the 2D case, Huang-Wang [11] investigated the global existence of strong solution with general large data in bounded domain provided that the some compatibility condition holds. Zhong [21] removed the compatibility condition, and established the large time behavior of strong solutions. Recently, Lv et al [13] showed the global existence of strong solutions to the 2D Cauchy problem with the large data and vacuum.…”

Section: Yang Liu Nan Zhou and Renying Guomentioning

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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“…Yang and Sun [21] got the global existence of weak solutions for any adiabatic exponent γ ≥ 1. Zhong [35] established the global existence and exponential decay of strong solutions to the initial boundary value problem of two-dimensional nonhomogeneous magnetohydrodynamic (MHD) equations with non-negative density.…”

Section: Introductionmentioning

confidence: 99%

Global strong solution to 3D full compressible magnetohydrodynamic flows with vacuum at infinity

Hou

Jiang

Peng

2021

Z. Angew. Math. Phys.

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Global strong solution and exponential decay for nonhomogeneous Navier-Stokes and magnetohydrodynamic equations

Cited by 9 publications

References 20 publications

Local well‐posedness to the 2D Cauchy problem of nonhomogeneous heat‐conducting Navier–Stokes and magnetohydrodynamic equations with vacuum at infinity

Local well‐posedness to the 2D Cauchy problem of nonhomogeneous heat‐conducting Navier–Stokes and magnetohydrodynamic equations with vacuum at infinity

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

Global strong solution to 3D full compressible magnetohydrodynamic flows with vacuum at infinity

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