Global solutions of a radiative and reactive gas with self‐gravitation for higher‐order kinetics

Abstract

The existence of global solutions is established for compressible Navier–Stokes equations by taking into account the radiative and reactive processes, when the heat conductivity κ (κ1(1 + θq) ≤ κ ≤ κ2(1 + θq),q ≥ 0), where θ is the temperature. This improves the previous results by enlarging the scope of q including the constant heat conductivity. Copyright © 2012 John Wiley & Sons, Ltd.

Global solutions to planar magnetohydrodynamic equations with radiation and large initial data

“…More recently, Umehara and Tani showed the global existence of a unique classical solution to a free boundary problem of the one-dimensional radiative and reactive gases. Subsequently, the result was extended by Qin and Yao [20] and Wang and Xie [31].…”

“…However, similar obstacle on q is also in existence even if we neglect the magnetic fields. For instance, Ducomet-Zlotnik [3] proved the existence and asymptotic behavior for 1D radiative and reactive gas when q ≥ 2 and Umehara-Tani [22,23] made further extension in this direction for 1D or spherically symmetric case when 3 ≤ q < 9, which extended to q ≥ 0 by authors in [16] . In addition, Wang and Xie [27] showed global existence of strong solutions for the Cauchy problem when q > 5 2 and the reference [4] proved global-in-time bounds of solutions and established it global exponential decay in the Lebegue and Sobolev spaces when q ≥ 2.…”