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

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arxiv 2502.17147 v1 pith:MOTNJOZS submitted 2025-02-24 math.AP

Paolo Antonelli , Didier Bresch , Stefano Spirito This is my paper · ORCID
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keywords viscositycoefficientequationsglobalnavier-stokes-kortewegpowersolutionsweak
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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.

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  1. Dissipative Solutions to a Compressible Non-Newtonian Korteweg System with Density-Dependent Viscous Stress Tensor

    math.AP 2026-01 accept novelty 6.0 of 10

    Global dissipative solutions and weak-strong uniqueness hold for a compressible non-Newtonian Navier–Stokes–Korteweg system with density-dependent viscosity on the torus in 2D and 3D.

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