Year: 2026
Type: preprint
Abstract: This paper is concerned with the conditional Hölder regularity of the temperature for the heat-conducting compressible Navier-Stokes system, where the pressure takes a complete form that includes the Stefan-radiation correction. Under minimal assumptions on the density and velocity, we prove that any weak solution automatically exhibits Hölder continuity in the temperature component. This constitutes the main result of the work and is achieved by an application of the De Giorgi method. As a consequence of this conditional regularity, we establish the global-in-time existence of a regular, unique solution to a simplified system for the compressible potential flow of a heat-conducting fluid, valid for arbitrarily large initial data.
Source: arXiv (Cornell University)
Institutions: University of Warsaw, Beijing Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Awards: G317705483, G9000372377
OpenAlex ID: W7222960367