The critical exponent for the dissipative plate equation with power nonlinearity

In this paper, we find the critical exponent of global small data solutions for a damped plate equation with power nonlinearity utt−Δutt+Δ2u+ut=|u|p,t≥0,x∈R2,and for a system of two weakly coupled damped plate equations. We show how assuming small data in the energy space H2×H1 and in L1 is sufficient to compensate the regularity-loss type decay effect created by the rotational inertia term −Δutt.