Global classical solutions and large-time behavior of the two-phase fluid model
Abstract
We study the global existence of a unique strong solution and its large-time behavior of a two-phase fluid system consisting of the compressible isothermal Euler equations coupled with compressible isentropic Navier-Stokes equations through a drag forcing term. The coupled system can be derived as the hydrodynamic limit of the Vlasov-Fokker-Planck/isentropic Navier-Stokes equations with strong local alignment forces. When the initial data is sufficiently small and regular, we establish the unique existence of the global -solutions in a perturbation framework. We also provide the large-time behavior of classical solutions showing the alignment between two fluid velocities exponentially fast as time evolves. For this, we construct a Lyapunov function measuring the fluctuations of momentum and mass from its averaged quantities.
Cite
@article{arxiv.1607.00177,
title = {Global classical solutions and large-time behavior of the two-phase fluid model},
author = {Young-Pil Choi},
journal= {arXiv preprint arXiv:1607.00177},
year = {2016}
}