Uniqueness of Solutions to a Gas-Disk Interaction System
arXiv:1903.09886 · doi:10.1007/s00205-019-01459-5
Abstract
In this paper we give an elementary proof of uniqueness of solutions to a gas-disk interaction system with diffusive boundary condition. Existence of near-equilibrium solutions for this type of systems with various boundary conditions has been extensively studied in [1-8, 10]. 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.
arXiv comment20 pages, 1 figure
References in corpus (5)
- Approach to Equilibrium of a Body Colliding Specularly and Diffusely with a Sea of Particles
- Velocity Reversal Criterion of a Body Immersed in a Sea of Particles
- Effects of concavity on the motion of a body immersed in a Vlasov gas
- Motion of a Rigid Body in a Special Lorentz Gas: Loss of Memory Effect
- Wall Effect on the Motion of a Rigid Body Immersed in a Free Molecular Flow