San Martín, Jorge Alonso; Starovoitov, Victor; Tucsnak, Marius Global weak solutions for the two-dimensional motion of several rigid bodies in an incompressible viscous fluid. (English) Zbl 1018.76012 Arch. Ration. Mech. Anal. 161, No. 2, 113-147 (2002). The authors study the motion of several inhomogeneous rigid bodies immersed in an incompressible inhomogeneous viscous fluid, all contained in a fixed open bounded subset of \(\mathbb{R}^2\). The fluid is governed by Navier-Stokes equations, whereas the rigid bodies move following Newton’s laws for linear and angular momentum. The novelty compared with previous existence results on the subject is that collisions are allowed – however, the space dimension is restricted to two. The global existence of weak solutions satisfying an energy estimate is proved. Collisions can occur (between different solids or between a solid and the boundary) but only with vanishing relative velocity and acceleration. In order to prove the theorem, a penalized problem is introduced and solved, compactness being obtained by Di Perna-Lions theory. A special attention is paid to the possibility of collisions, namely in the proof of the compactness of velocity field. Reviewer: Isabell Gallagher (Palaiseau) Cited in 1 ReviewCited in 107 Documents MSC: 76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids 70E99 Dynamics of a rigid body and of multibody systems 35Q30 Navier-Stokes equations Keywords:immersed rigid bodies; Navier-Stokes equations; Newton’s laws; collisions; global existence of weak solutions; energy estimate; compactness; Di Perna-Lions theory; penalization PDFBibTeX XMLCite \textit{J. A. San Martín} et al., Arch. Ration. Mech. Anal. 161, No. 2, 113--147 (2002; Zbl 1018.76012) Full Text: DOI