Generation of semigroups for the thermoelastic plate equation with free boundary conditions

We consider the linear thermoelastic plate equations with free boundary conditions in uniform $C^4$-domains, which includes the half-space, bounded and exterior domains. We show that the corresponding operator generates an analytic semigroup in $L^p$-spaces for all $p\in (1,\mathrm{\infty })$ and has maximal $L^q$-$L^p$-regularity on finite time intervals. On bounded $C^4$-domains, we obtain exponential stability.