Navier-Stokes flow around a rotating obstacle. Mathematical analysis of its asymptotic behavior (Q311365)

The authors present the mathematical analysis of motions of a viscous incompressible fluid around a moving rigid body, supposing that the motion consists in a constant velocity translation and a constant angular velocity rotation.NEWLINENEWLINEThey first present (Chapters 1 and 2) the equations (incompressible Navier-Stokes system) in the particular framework of a moving domain and show how these equations can be transformed into a modified system (MNS) with additional terms, in a fixed domain.NEWLINENEWLINEThen (Chapters 3 and 4) the authors study fundamental solutions of the corresponding Oseen (linearized around a constant rest state) system, in the non-steady as well in the steady cases, together with their main properties and the associated estimates.NEWLINENEWLINEIn Chapters 5 and 6, a useful representation formula is established for the complete MNS system in an exterior domain, and its asymptotic properties are derived.NEWLINENEWLINEIn Chapter 7, Leray's solutions for the linearized problems are studied through their respective representation formulae, and the last part (Chapter 8) contains more recent results on Leray's solutions for the nonlinear stationary problem.