Global weak solutions of the Navier-Stokes-Korteweg equations in one dimension

Journal de Mathématiques Pures et Appliquées 2026 Open access

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Authors: Paolo Antonelli, Didier Bresch, Stefano Spirito
DOI: 10.1016/j.matpur.2026.103952
Cited by: 0
References: 72

Abstract

We prove the global existence of weak solutions of the one-dimensional Navier-Stokes-Korteweg (NSK) equations when the viscosity and the capillarity coefficients are power functions of the density, which may be zero on a set with positive measure. The proofs are based on a truncation argument combined with the Energy estimate and BD Entropy. Notably, we do not require any upper bound on the exponent of the power of the viscosity coefficient. In particular, we are able to consider very degenerate viscosity coefficient and to substantially improve previous results.

Fields of Study & Subjects

Navier-Stokes equation solutions Advanced Mathematical Physics Problems Stability and Controllability of Differential Equations

Publication details

Journal / source
Journal de Mathématiques Pures et Appliquées
Publisher
Elsevier BV
Volume
215
Pages
103952–103952
Publication date
18 June 2026
Language
EN