Abstract
In this paper, we study the thermally radiative magnetohydrodynamic equations in 3D, which describe the dynamical behaviors of magnetized fluids that have nonignorable energy and momentum exchange with radiation under the nonlocal thermal equilibrium case. By using exquisite energy estimate, global existence and uniqueness of classical solutions to Cauchy problem in ℝ3 or T3 are established when initial data is a small perturbation of some given equilibrium. We can further prove that the rates of convergence of solution toward the equilibrium state are algebraic in ℝ3 and exponential in T3 under some additional conditions on initial data. The proof is based on the Fourier multiplier technique.
Highlights
In the study of plasma physics, due to the high temperature and high pressure environment, the motion of charged particles flow is usually regarded as compressible fluids, and their dynamics is very often shaped and controlled by magnetic fields and high temperature radiation effects
When the distribution of photon is almost isotropic, based on the standard hydrodynamics, such dynamics can be described by the following 3D thermally radiative magnetohydrodynamic equations: ρt + div ðρuÞ = 0, ρðut
∥ðρ, u, H, Θ, ηÞ∥2H4 , and completes the proof of Theorem 11
Summary
In the study of plasma physics, due to the high temperature and high pressure environment, the motion of charged particles flow is usually regarded as compressible fluids, and their dynamics is very often shaped and controlled by magnetic fields and high temperature radiation effects. When the magnetic is ignored (i.e., H = 0 in (1)), system (1) can be reduced to the nonequilibrium diffusion approximation model in radiation hydrodynamics This model describes the energy flow due to radiative process in a Journal of Function Spaces semiquantitative sense and is accurate if the specific intensity of radiation is almost isotropic (cf [3,4,5]). We are focused on the asymptotic and global existence of classical solutions of system (1) with the initial data: ðρ, u, H, θ, nÞjt=0 = ðρ0, u0, H0, θ0, n0ÞðxÞ, x ∈ Ω: ð3Þ. We shall use ∥·∥ to denote norm L2ðR3Þ
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