Motion of slightly compressible fluids in a bounded domain. II
Analysis of PDEs
2017-07-19 v2 Differential Geometry
Functional Analysis
Fluid Dynamics
Abstract
We study the problem of inviscid slightly compressible fluids in a bounded domain. We find a unique solution to the initial-boundary value problem and show that it is near the analogous solution for an incompressible fluid provided the initial conditions for the two problems are close. In particular, the divergence of the initial velocity of the compressible flow at time zero is assumed to be small. Furthermore we find that solutions to the compressible motion problem in Lagrangian coordinates depend differentiably on their initial data, an unexpected result for this type of non-linear equations.
Keywords
Cite
@article{arxiv.1309.0477,
title = {Motion of slightly compressible fluids in a bounded domain. II},
author = {Marcelo M. Disconzi and David G. Ebin},
journal= {arXiv preprint arXiv:1309.0477},
year = {2017}
}
Comments
to appear in Communications in Contemporary Mathematics