Global existence of solutions for a parabolic systems with logarithmic nonlinearity

The primary goal of this paper is to study the global existence and blow-up of solutions in a finite time for a class of parabolic systems that are characterized by the fractional p-Laplacian operator with logarithmic nonlinearity. By employing the classical Galerkin method, we show the existence and decay exponential estimates of the global weak solutions with critical initial energy \(J(u_0,v_0)<d\) $J(u_0,v_0)<d$ . Moreover, we discuss the finite time blow up of weak solutions.