Work

Uniqueness of solutions to the 2D compressible Navier-Stokes equations for bounded densities

Year: 2026

Type: preprint

Abstract: We prove the uniqueness of global solutions to the two dimensional barotropic compressible Navier--Stokes equations within the regularity class introduced by Danchin and Mucha [14], for general $C^1$ pressure laws. A crucial assumption is that both solutions have bounded divergence, locally integrable in time, which ensures that their densities remain bounded without excluding vacuum or requiring spatial regularity of the density.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.18178

Authors: Pescatore, Lorenzo, Violini, Alessandro

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: Universität Basel, Istituto Nazionale di Alta Matematica "Francesco Severi", Deutsche Forschungsgemeinschaft, Gruppo Nazionale per l'Analisi Matematica, la Probabilità e le loro Applicazioni

Award: G3044548687

OpenAlex ID: W7221801230

Cites: 3

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Related to: 10