Work

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

Year: 2026

Type: article

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.

Source: Journal de Mathématiques Pures et Appliquées

DOI: 10.1016/j.matpur.2026.103952

Authors: Paolo Antonelli, Didier Bresch, Stefano Spirito

Institutions: Gran Sasso Science Institute, Centre National de la Recherche Scientifique, Le LAMA, Université Savoie Mont Blanc, University of L'Aquila

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $2,900