Global existence and infinite time blow-up of a fractional Laplacian equation with logarithmic nonlinearity

In this paper, we study the Cauchy problem of fractional Laplacian equations with logarithmic nonlinearity. By employing the potential well method and a logarithmic Sobolev inequality, we obtain the global existence and infinite time blow-up of solutions under suitable conditions. Moreover, we consider the asymptotic behavior of solutions and obtain some decay estimates.