Global Existence and Large Time Behavior of Strong Solutions for 3D Nonhomogeneous Heat-Conducting Magnetohydrodynamic Equations

• Published in: The Journal of geometric analysis Vol. 31; no. 11; pp. 10648 - 10678
• Main Author: Zhong, Xin
• Format: Journal Article
• Language: English
• Published: New York Springer US 01-11-2021; Springer Nature B.V
• Subjects: Abstract Harmonic Analysis; Boundary conditions; Boundary value problems; Convex and Discrete Geometry; Decay rate; Differential Geometry; Dynamical Systems and Ergodic Theory; Fluid flow; Fourier Analysis; Geometry; Global Analysis and Analysis on Manifolds; Heat transfer; Heat transmission; Magnetohydrodynamic equations; Magnetohydrodynamics; Mathematical analysis; Mathematics; Mathematics and Statistics; 76D03; Nonhomogeneous heat-conducting magnetohydrodynamic equations; Vacuum; Large time behavior; 76W05; Global strong solution
• ISSN: 1050-6926; 1559-002X
• DOI: 10.1007/s12220-021-00661-w

We are concerned with an initial boundary value problem of nonhomogeneous heat-conducting magnetohydrodynamic equations in a bounded simply connected smooth domain
Ω
⊆
R
3
, with Navier-slip boundary conditions for the velocity and magnetic field and Neumann boundary condition for the temperature. We prove the global existence of a unique strong solution provided that
‖
ρ
0
u
0
‖
L
2
2
+
‖
b
0
‖
L
2
2
‖
curl
u
0
‖
L
2
2
+
‖
curl
b
0
‖
L
2
2
is suitably small. Moreover, we also obtain large time decay rates of the solution.