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

Abstract

We study positive radial solutions of quasilinear elliptic systems with a gradient term in the form where is either a ball or the whole space, , , , and . We first classify all the positive radial solutions in case is a ball, according to their behavior at the boundary. Then we obtain that the system has non-constant global solutions if and only if and . 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.