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

  • Mengkun ZhuEmail author
  • Mingtong Ou
Article
  • 23 Downloads

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.

Keywords

Heat-conducting Magnetohydrodynamic flows Density-temperature-dependent viscosity and resistivity Decay Vacuum 

Mathematics Subject Classification 2010

35B45 76D03 76D05 76W05 

Notes

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© Springer Nature B.V. 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsQilu University of Technology (Shandong Academy of Sciences)JinanPeople’s Republic of China
  2. 2.School of Mathematical SciencesHuaqiao UniversityQuanzhouPeople’s Republic of China

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