Global strong solutions to the 3D incompressible heat-conducting magnetohydrodynamic flows

M Zhu, M Ou - Mathematical Physics, Analysis and Geometry, 2019 - Springer
M Zhu, M Ou
Mathematical Physics, Analysis and Geometry, 2019Springer
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 Ω⊂ ℝ 3 Ω⊂R^3. Let ρ
0, u 0, b 0 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∥ ρ 0 u 0∥ L 2 2+∥ b 0∥ L 2 2 …
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 . 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 is small. Moreover, we establish some decay estimates for the strong solutions.
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