Asymptotic behavior of blowing-up radial solutions for quasilinear elliptic systems arising in the study of viscous, heat conducting fluids

In this paper, we deal with the following quasilinear elliptic system involving gradient terms in form: $$ \begin{cases} \Delta_p u= v^m| \nabla u |^\alpha & \text{in}\quad \Omega\\ v= v^\beta| |^q \Omega, \end{cases} where $\Omega\subset\mathbb{R}^N\ (N\geq 1)$ is either equal to $ \mathbb{R}^N or a ball $B_R$ centered at origin and having radius $R>0$, $1 < p \infty$, $m,q > 0$, $\alpha\geq $0\leq \beta\leq m$ $\delta:=(p-1-\alpha)(p-1-\beta)-qm \neq 0$. Our aim establish asymptotics of blowing-up radial solutions above system. Precisely, provide accurate asymptotic behavior boundary for such solutions. For that, prove strong maximal principle problem independent interest study an auxiliary asymptotically autonomous $\mathbb{R}^3$.