The dispersive effect of the Coriolis force for the stationary and non-stationary Navier-Stokes equations is investigated. Existence of a unique solution is shown for arbitrary large external force provided the Coriolis force is large enough. In addition to the stationary case, counterparts of several classical results for the nonstationary Navier-Stokes problem have been proven. The analysis is carried out in a new framework of the Fourier-Besov spaces.

Abstract. The paper investigates the issue of existence of solutions to the stationary Navier-Stokes equations in a two dimensional bounded domain. The system is studied with nonhomogeneous slip boundary conditions admitting flow across the boundary. The main result proves the existence of weak solutions for arbitrary data. An advantage of our approach is that the proof is constructive. Properties of the obtained result allow to study turbulent flows in description of such phenomena as polymers and blood motion. MSC: 35Q30, 75D05

Abstract. We construct L p -estimates for the inhomogeneous Oseen system studied in a two dimensional exterior domain Ω with inhomogeneous slip boundary conditions. The kernel of the paper is a result for the half space R 2 + . Analysis of this model system shows us a parabolic character of the studied problem, resulting as an appearance of the wake region behind the obstacle. Main tools are given by the Fourier analysis to obtain the maximal regularity estimates. The results imply the solvability for the Navier-Stokes system for small velocity at infinity. MSC: 35Q30, 75D07

The paper analyzes the issue of existence of solutions to linear problems in two dimensional exterior domains, linearizations of the Navier-Stokes equations. The systems are studied with a slip boundary condition. The main results prove the existence of distributional solutions for arbitrary data.

Abstract. We investigate a steady flow of incompressible fluid in the plane. The motion is governed by the Navier-Stokes equations with prescribed velocity u ∞ at infinity. The main result shows the existence of unique solutions for arbitrary force, provided sufficient largeness of u ∞ . Furthermore a spacial structure of the solution is obtained in comparison with the Oseen flow. A key element of our new approach is based on a setting which treats the directino of the flow as time direction. The analysis is done in framework of the Fourier transform taken in one (perpendicular) direction and a special choice of function spaces which take into account the inhomogeneous character of the symbol of the Oseen system. From that point of view our technique can be used as an effective tool in examining spatial asymptotics of solutions to other systems modeled by elliptic equations. MSC: 35Q30, 75D05

The paper examines the issue of existence of solutions to the steady Navier-Stokes equations in an exterior domain in R 2 . The system is studied with nonhomogeneous slip boundary conditions. The main results proves the existence of weak solutions for arbitrary data.

Abstract. We study steady flow of a second grade fluid past an obstacle in three space dimensions. We prove existence of solution in weighted Lebesgue spaces with anisotropic weights and thus existence of the wake region behind the obstacle. We use properties of the fundamental Oseen tensor together with results achieved in [6] and properties of solutions to steady transport equation to get up to arbitrarily small ε the same decay as the Oseen fundamental solution.

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