Viscous pressureless flows with free boundary in one space dimension: The constant viscosity case
Abstract
We establish the global well-posedness of the free boundary problem of the viscous pressureless and almost pressureless heat conductive flows in one space dimension. In both cases, arbitrarily large but smooth initial data is considered, and the evolving fluid domains remain bounded for all time. In the viscous pressureless case, we are able to identify the terminal flow domain in terms of the initial data. In the viscous almost pressureless case, we construct the flow as a perturbation of the viscous pressureless flow, and establish the first result for the Navier-Stokes-Fourier system in the current setting.
Fields of Study & Subjects
Navier-Stokes equation solutions
Stability and Controllability of Differential Equations
Nonlinear Partial Differential Equations
Publication details
- Journal / source
- Journal of Mathematical Analysis and Applications
- Volume
- 565
- Issue
- 1
- Pages
- 130933–130933
- Publication date
- 10 July 2026
- Language
- EN