2015/01/29 by Juhi Jang, Ian Tice, Jang, Juhi +3
Engineering · Mathematics · #35R35 #76E19 #76N10 #76N99 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Primary 35Q30 #Secondary 76E17
paper · pdf · doi:10.48550/arxiv.1501.07577
openalex publication_date 2015/01/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This paper concerns the dynamics of two layers of compressible, barotropic, viscous fluid lying atop one another. The lower fluid is bounded below by a rigid bottom, and the upper fluid is bounded above by a trivial fluid of constant pressure. This is a free boundary problem: the interfaces between the fluids and above the upper fluid are free to move. The fluids are acted on by gravity in the bulk, and at the free interfaces we consider both the case of surface tension and the case of no surface forces. We prove that the problem is locally well-posed. Our method relies on energy methods in Sobolev spaces for a collection of related linear and nonlinear problems.