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Global Strong Solutions to the 3D Incompressible Heat-Conducting Magnetohydrodynamic Flows

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Abstract

In this article, we prove that there exists a global strong solution to the 3D inhomogeneous incompressible heat-conducting magnetohydrodynamic equations with density-temperature-dependent viscosity and resistivity coefficients in a bounded domain \({\Omega } \subset \mathbb {R}^{3}\). Let ρ0, u0, b0 be the initial density, velocity and magnetic, respectively. Through some time-weighted a priori estimates, we study the global existence of strong solutions to the initial boundary value problem under the condition that \(\|\sqrt {\rho _{0}} u_{0}\|_{L^{2}}^{2} + \|b_{0}\|_{L^{2}}^{2}\) is small. Moreover, we establish some decay estimates for the strong solutions.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Qilu University of Technology (Shandong Academy of Sciences), Jinan, 250353, Shandong Province, People’s Republic of China

    Mengkun Zhu

  2. School of Mathematical Sciences, Huaqiao University, Quanzhou, 362021, Fujian Province, People’s Republic of China

    Mingtong Ou

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  1. Mengkun Zhu
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  2. Mingtong Ou
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Zhu, M., Ou, M. Global Strong Solutions to the 3D Incompressible Heat-Conducting Magnetohydrodynamic Flows. Math Phys Anal Geom 22, 8 (2019). https://doi.org/10.1007/s11040-019-9306-8

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