Weak solutions to incompressible heat-conducting motions with large flux

Joanna Renc{\l}awowicz; Wojciech M. Zaj\k{a}czkowski

REVIEW

Not yet reviewed by Pith; the record is open.

Re-run · record.json Download PDF Read on arXiv ↗

This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.

SPECIMEN: schema-true, not a live event

T0 review · schema-true

One-sentence machine reading of the paper's core claim.

pith:XXXXXXXX · record.json · timestamp

arxiv 2506.22155 v1 pith:5EGKAWBA submitted 2025-06-27 math.AP

Weak solutions to incompressible heat-conducting motions with large flux

Joanna Renc{\l}awowicz , Wojciech M. Zaj\k{a}czkowski This is my paper

classification math.AP

keywords estimateincompressibleinflowlargeoutflowsolutionsweakanalyze

verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

0 comments

read the original abstract

We analyze the problem for viscous incompressible heat-conduc\-ting fluid in a finite cylinder with large inflow and outflow, modelled with Navier-Stokes equations coupled with the heat equation. We prove energy estimate without restrictions on the magnitudes of the external force, initial data, inflow and outflow. In order to estimate nonlinear terms we use weighted spaces. Next, using Galerkin approximation, we show existence of weak solutions.

Weak solutions to incompressible heat-conducting motions with large flux

discussion (0)