Global and blow-up radial solutions for quasilinear elliptic systems arising in the study of viscous, heat conducting fluids

We study positive radial solutions of quasilinear elliptic systems with a gradient term in the form {Delta(p)u( )= v(m) vertical bar del u vertical bar(alpha)( in Omega,) Delta(p)v = v(beta)vertical bar del u vertical bar(q )in Omega, where Omega subset of R-N (N >= 2) is either a ball or the whole space, 1 < p < infinity, m, q > 0, alpha >= 0, 0 <= beta <= m in and (p - 1 - alpha)(p - 1 - beta) - qm not equal 0. We first classify all the positive radial solutions in case Omega is a ball, according to their behavior at the boundary. Then we obtain that the system has nonconstant global solutions if and only if 0 <= alpha < p -1 and mq < (p -1 -alpha) (p -1 -beta). Finally we, describe the precise behavior at infinity for such positive global radial solutions by using properties of three component cooperative and irreducible dynamical systems.