Global-in-time existence of finite energy weak solutions to a relaxed Navier-Stokes-Korteweg model

Florian Oschmann; Florian Wendt

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arXiv · 2608.12969

Global-in-time existence of finite energy weak solutions to a relaxed Navier-Stokes-Korteweg model

Florian Oschmann·Florian Wendt

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Abstract

We consider a parabolic relaxation formulation of the compressible Navier-Stokes-Korteweg system and prove the global-in-time existence of finite energy weak solutions to the associated initial-boundary-value-problem. Our proof is based on a three-level approximation scheme, a weak compactness property of the effective viscous flux, and parabolic regularity estimates. Our result holds for a broad variety of non-monotone pressure functions and generalizes the corresponding results known for the compressible Navier-Stokes equations to the relaxation system.

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Florian Oschmann, Florian Wendt. 2026-08-13. Global-in-time existence of finite energy weak solutions to a relaxed Navier-Stokes-Korteweg model. https://arxiv.org/abs/2608.12969

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