Global Weak Solutions for Perfect-Gas Navier-Stokes-Fourier Flow

Definitions and mathematical statement

Let $p$, $\rho$, and $\vartheta$ denote pressure, mass density, and absolute temperature, respectively. The supplied perfect-gas pressure law is \[ p=\rho\vartheta. \] The record does not specify the domains or admissible values of these fields.

Reconstructed target supplied by the registry. Establish global-in-time existence of weak solutions to the compressible Navier--Stokes--Fourier system with this pressure law, without the additional structural restrictions required by existing results.

Unresolved formulation. This target cannot yet be expressed as a complete quantified existence statement. The supplied original excerpt says only that an issue involving the perfect-gas law is open. It does not identify the governing equations, spatial dimension or domain, initial and boundary conditions, admissible initial data, remaining constitutive relations, definition of weak solution, or the structural restrictions intended to be removed. The pressure relation alone does not specify the complete thermodynamic model. Accordingly, no particular choices of these hypotheses, or universal quantification over unspecified data, are asserted here. The reconstructed target requires recovery of its full source context before mathematical formalization.

Short English statement

The supplied reconstructed problem asks for global weak solutions of compressible Navier--Stokes--Fourier flow with $p=\rho\vartheta$, under fewer structural assumptions. The original excerpt is too incomplete to determine the precise existence claim. The registry labels the problem open; this draft does not independently verify that status.

Sources

• Local problem registry, supplied record: permanent UnsolvedMath ID $30005824$, exact source problem code catalogue entry; title: Global Weak Solutions for Perfect-Gas Navier--Stokes--Fourier Flow. The record belongs to the Oberwolfach Reports Open Problems collection and gives proposed year 2024. No individual proposer is supplied.
• Supplied report attribution: Hyperbolic Balance Laws: Interplay between Scales and Randomness (2024), Oberwolfach Reports, pp. 567--656, DOI 10.4171/owr/2024/10. Supplied source URL and literature-source link, labeled "Oberwolfach Report 10/2024": https://doi.org/10.4171/owr/2024/10. The extracted fragment includes the page marker 633.
• Supplied literature assessment, checked 2026-08-22: the extracted text is only a fragment about the perfect-gas law, with no complete theorem or hypotheses identified; the assessment reports that no contrary resolution could be verified. This is supplied dated curation derived from the OWR record, not an independently verified literature assessment. Time-sensitive status and cited claims require independent verification.
• The registry assigns statement status corrected_verified and reports that its reconstructed statement was checked against the official Oberwolfach report. This is a supplied verification claim, not verification performed for this draft; its relationship to the fragment-only literature assessment remains unresolved.