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We study the asymptotic behavior of solutions to the incompressible Navier-Stokes system considered on a sequence of spatial domains, whose boundaries exhibit fast oscillations with amplitude and characteristic wave length proportional to a small parameter. Imposing the complete slip boundary conditions we show that in the asymptotic limit the fluid sticks completely to the boundary provided the oscillations are nondegenerate, meaning not oriented in a single direction.

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We consider the compressible (barotropic) Navier-Stokes system on time dependent domains, supplemented with slip boundary conditions. Our approach is based on penalization of the boundary behavior, viscosity, and the pressure in the weak formulation. Global-in-time weak solutions are obtained.

We study the homogenization problem for the evolutionary Navier-Stokes system under the critical size of obstacles. Convergence towards the limit system of Brinkman's type is shown under very mild assumptions concerning the shape of the obstacles and their mutual distance.

We consider the motion of a fluid in the exterior of a rotating obstacle. This leads to a modified version of the Stokes system which we consider in the whole space R n , n = 2 or n = 3 and in an exterior domain D ⊂ R 3. For every q ∈ (1, ∞) we prove existence of solutions and estimates in function spaces with weights taken from a subclass of the Muckenhoupt class A q. Moreover, uniqueness is shown modulo a vector space of dimension 3.

We consider a simplified model arising in radiation hydrodynamics based on the Navier-Stokes-Fourier system describing the macroscopic fluid motion, and a transport equation modeling the propagation of radiative intensity. We establish global-in-time existence for the associated initial-boundary value problem in the framework of weak solutions.

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