Estimates of Perturbed Oseen Semigroups and Their Applications to the Navier–Stokes System in $\mathbb{R}^n$

For perturbed Oseen semigroups in $\mathbb{R}^n$, we establish their power $L_p-L_q$ estimates. These estimates are used to prove the existence of small global solutions to perturbed nonlinear Oseen systems and also of estimates of their $L_p$-norms as $t\to \infty$.