Abstract
In this paper we consider the motion of a rigid body in a viscous incompressible fluid when some Navier slip conditions are prescribed on the body’s boundary. The whole “viscous incompressible fluid + rigid body” system is assumed to occupy the full plane ℝ 2 . We prove the existence of global-in-time weak solutions with constant non-zero circulation at infinity.
Highlights
The problem of well-posedness of Navier–Stokes equations with infinite energy in dimension two has been studied a lot in the past years
The first result deals with solutions defined in R3, the second one defined in the half space R3+
For exterior domains, where no slip boundary condition is prescribed on the boundary, it was proved in [15] an existence result for initial data in the weak-L2 space with some restriction on the concentration of the initial energy
Summary
The problem of well-posedness of Navier–Stokes equations with infinite energy in dimension two has been studied a lot in the past years. For exterior domains, where no slip boundary condition is prescribed on the boundary, it was proved in [15] an existence result for initial data in the weak-L2 space with some restriction on the concentration of the initial energy. These solutions will remain uniformly bounded in weak-L2 norm for almost every time and bounded in the K4 norm which is the Kato norm for p = 4. We study the Cauchy problem for a system describing the motion of a rigid body immersed in a viscous incompressible fluid when some Navier slip conditions are prescribed on the body’s boundary. At this moment it is not clear if the analysis from [1] can be adapted in the fluid-structure interaction problem (1)-(8)
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