Global Weak Solutions¶for the Two-Dimensional Motion¶of Several Rigid Bodies¶in an Incompressible Viscous Fluid

Feedback stabilization of a simplified 1d fluid–particle system

“…This system is a simplified model corresponding to the motion of a rigid body into a viscous incompressible fluid (see [24,10,11,9,19,25,15,17] for some references). In our case, we replace the Navier-Stokes system by the viscous Burgers equation and the rigid body is reduced to a point particle.…”

On the Motion of Several Rigid Bodies in a Viscous Multipolar Fluid

“…To the best of our knowledge, this issue remains largely open even for a two-dimensional physical domain Ω. In the 2-D case, however, there is a remarkable result by San Martin et al [18] stating, in particular, that possible collisions, if any, must be "smooth", that means, with zero relative velocities. Another strong evidence of absence of collisions in the 2-D geometry is provided independently by Hesla [10] and Hillairet [11].…”

“…Suitable approximate solutions are constructed in Section 4 by means of a scheme similar to that used in [6]. In particular, the method of construction is based on the idea of San Martin et al [18], where the rigid objects are approximated by a fluid of large viscosity. Such an approach is of course intimately related to our choice of the boundary conditions specified through (1.11), (1.12).…”

Four variations in global Carleman weights applied to inverse and controllability problems

“…The total angle θ associated to the angular velocity r is defi ned by θ(t) = θ 0 + t 0 r (s) ds, where θ 0 ∈ R complements the initial data. The existence of solutions and regularity for this system has been recently studied in several papers (see [39], [41] and the references therein).…”