Global Existence and Asymptotic Behavior of Cylindrically Symmetric Solutions for the 3D Infrarelativistic Model with Radiation

Global existence and asymptotic behavior of spherically symmetric solutions for the multi-dimensional infrarelativistic model

“…Recently, Azevedo, Sauter and Thompson [1] also studied an approximation model of compressible radiative flow and established global classical solutions for this model in a slab under semi-reflexive boundary conditions using energy-entropy estimates and a homotopic version of the Leray-Schauder fixed point theorem together with classical Friedman-Schauder estimates for linear second order parabolic equations in boundary Hölder spaces. Qin and Zhang [24] obtained global existence and asymptotic behavior of cylindrically symmetric solutions for the 3D infrarelativistic model with radiation.…”

“…The next two lemmas are aimed at showing the asymptotic behavior of solutions to the problem (24) with the initial boundary conditions (18)- (20)…”

“…Estimate (125) has been obtained in Lemma 1.3.1 of [23]. Differentiating (24) 3 with respect to t and multiplying the result by θ t over [0, L], we have that for any ε > 0,…”

“…Using the Gagliardo-Nirenberg interpolation inequality and Young's inequality, we derive from (24) 3 that…”

“…Assume that the initial data (v 0 , u 0 , θ 0 , I 0 ) ∈ H 1 and the compatibility conditions hold. Then there exists a unique global solution (24) with initial boundary value conditions (18)- (20) verifying for all (…”