Linearized stationary incompressible flow around rotating and translating bodies: Asymptotic profile of the velocity gradient and decay estimate of the second derivatives of the velocity

We consider a system arising by linearization of a model for stationary viscous incompressible flow around a translating and rotating body. An asymptotic profile of the gradient of the velocity is derived. The leading term of the profile involves derivatives of a fundamental solution constructed by R.B. Guenther and E.A. Thomann (2006) [23], for the system in question. In addition, we establish decay estimates of the second derivatives of the velocity.