46 research outputs found
Hypocoercivity of the linearized BGK-equation with stochastic coefficients
In this paper we study the effect of randomness on a linearized BGK-model in
one dimension. We prove exponential decay rate to a global equilibrium. This
decay rate can be proven to be independent of the stochastic influence in a
physical reasonable norm. We will further discuss the decay rate of the -th
derivative with respect to the stochastic variable of the solutions. Our
strategy is based on Lyapunov's method. The matrices we need for a Lyapunov's
estimate now depend on the stochastic variable. This requires a careful
analysis of the random effect
Local sensitivity analysis for the Cucker-Smale model with random inputs
We present pathwise flocking dynamics and local sensitivity analysis for the
Cucker-Smale(C-S) model with random communications and initial data. For the
deterministic communications, it is well known that the C-S model can model
emergent local and global flocking dynamics depending on initial data and
integrability of communication function. However, the communication mechanism
between agents are not a priori clear and needs to be figured out from observed
phenomena and data. Thus, uncertainty in communication is an intrinsic
component in the flocking modeling of the C-S model. In this paper, we provide
a class of admissible random uncertainties which allows us to perform the local
sensitivity analysis for flocking and establish stability to the random C-S
model with uncertain communication.Comment: 32 page
Error estimates of a bi-fidelity method for a multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with random inputs
Uniform error estimates of a bi-fidelity method for a kinetic-fluid coupled
model with random initial inputs in the fine particle regime are proved in this
paper. Such a model is a system coupling the incompressible Navier-Stokes
equations to the Vlasov-Fokker-Planck equations for a mixture of the flows with
distinct particle sizes. The main analytic tool is the hypocoercivity analysis
for the multi-phase Navier-Stokes-Vlasov-Fokker-Planck system with
uncertainties, considering solutions in a perturbative setting near the global
equilibrium. This allows us to obtain the error estimates in both kinetic and
hydrodynamic regimes