Compressible fluids and active potentials
Analysis of PDEs
2019-11-26 v2
Abstract
We consider a class of one dimensional compressible systems with degenerate diffusion coefficients. We establish the fact that the solutions remain smooth as long as the diffusion coefficients do not vanish, and give local and global existence results. The models include the barotropic compressible Navier-Stokes equations, shallow water systems and the lubrication approximation of slender jets. In all these models the momentum equation is forced by the gradient of a solution-dependent potential: the active potential. The method of proof uses the Bresch-Desjardins entropy and the analysis of the evolution of the active potential.
Cite
@article{arxiv.1803.04492,
title = {Compressible fluids and active potentials},
author = {Peter Constantin and Theodore D. Drivas and Huy Q. Nguyen and Federico Pasqualotto},
journal= {arXiv preprint arXiv:1803.04492},
year = {2019}
}
Comments
The classes of constitutive laws for the pressure and the viscosity have been extended; typos fixed