The critical exponent for the dissipative plate equation with power nonlinearity (Q1643252)

In this paper, the authors find the critical exponent of global small data solutions for a damped plate equation with power nonlinearity: \[ u_{tt}-\Delta u_{tt}+\Delta^2 u+u_t=|u|^p,t\geq 0, x\in R^2 \] and for a system of two weakly coupled damped plate equations. They show how assuming small data in the energy space \(H^2\times H^1\) and in \(L^1\) is sufficient to compensate the \textit{regularity-loss} type decay effect created by the rotational inertia term \(-\Delta u_{tt}\).