The motion of the rigid body in the viscous fluid including collisions. Global solvability result. (April 2017)

• Record Type: Journal Article
• Authors: Chemetov, Nikolai V.; Nečasová, Šárka
• Is Part Of: Nonlinear analysis. Volume 34(2017)
• Page Start: 416
• Page End: 445
• Publication Date: 2017-04
• Subjects: Rigid body -- Global weak solution -- Collisions in finite time; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2016.09.011
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: We shall consider the problem of the motion of a rigid body in an incompressible viscous fluid filling a bounded domain. This problem was studied by several authors. They mostly considered classical non-slip boundary conditions, which gave them very paradoxical result of no collisions of the body with the boundary of the domain. Only recently there are results when the Navier type of boundary is considered. In our paper we shall consider the Navier condition on the boundary of the body and the non-slip condition on the boundary of the domain. This case admits collisions of the body with the boundary of the domain. We shall prove the global existence of weak solution of the problem.