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Global well-posedness for the compressible Euler–Korteweg equations with damping in L2 - Lp critical Besov space and relaxation limit

Nonlinear Analysis: Real World Applications, ISSN: 1468-1218, Vol: 84, Page: 104274
2025
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Article Description

In this paper, we investigate the Cauchy problem of compressible Euler–Korteweg equations with damping. The global well-posedness is established in L2 - Lp critical Besov spaces. In our results, the existence theorem provides us with bounds that are independent of the relaxation parameter ɛ and capillary coefficient k. As a consequence, we rigorously justify the relaxation limit and study the effect of the Korteweg-type dispersion on the relaxation limit. Specially, when k≡0, our theorems reduce to the results in Crin-Barat and Danchin (2022) [28,29] on the Euler system with damping, and the smallness assumption for low-frequency initial data of velocity is weaker in some way.

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