Uniqueness of Solutions to a Gas-Disk Interaction System.

In this paper we give an elementary proof of the uniqueness of solutions to a gas-disk interaction system with diffusive boundary condition. The existence of near-equilibrium solutions for this type of system with various boundary conditions has been extensively studied in Aoki et al. (ESAIM:M2AN 42:26–275, 2008), Caprino et al. (Commun Math Phys 264: 167–189, 2006; Math Models Methods Appl Sci 17(9):1369–1403, 2007), Cavallaro (Rend Mat Ser VII 27:123–145, 2007), Chen and Strauss (Arch Ration Mech Anal 211:879–910, 2014; Commun Math Phys 338:139–168, 2015), Koike (J Stat Phys 172:795–823, 2018a; Kinet. Relat. Model 11(3): 441–467, 2018b) and Sisti and Ricciuti (SIAM J Math Anal 46(6):3579–3611, 2014). However, the uniqueness has been an open problem, even for solutions near equilibrium. Our work gives the first rigorous proof of the uniqueness among solutions that are only required to be locally Lipschitz; in particular, it holds for solutions far from equilibrium states. [ABSTRACT FROM AUTHOR]