Recently, it has been proved in Galakhov et al. (2016) that if either d80f33203d2f5888" title="Click to view the MathML source">α>m+γ−1 or α=m+γ−1 and 541b1d46e87c31b53dced1ba64762">, for any given this system possesses a global and bounded classical solution. The present work further shows that the same conclusion still holds for the critical case α=m+γ−1 and .