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This is a Quantitative Study study.

October 8, 2025Open Access

On the time-decay with the diffusion wave phenomenon of the solution to the compressible Navier-Stokes-Korteweg system in critical spaces

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Analysis explores time-decay estimates for solutions of the Navier-Stokes-Korteweg equations, suggesting stability around equilibrium states.

Global-in-time solutions around constant equilibrium states were established, indicating that stability is achievable.
Time-decay estimates in critical spaces highlight the behavior of solutions under perturbations at equilibrium states.
The study utilized Fourier-Besov norms to analyze diffusion wave properties, suggesting strong damping effects on solutions.
The findings imply that the compressible Navier-Stokes-Korteweg system can exhibit controlled behavior in critical spaces.

Kobayashi et al. (2025) studied this question.

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Analysis explores time-decay estimates for solutions of the Navier-Stokes-Korteweg equations, suggesting stability around equilibrium states.