Finite-time blow-up for the compressible Euler–Korteweg system with density-dependent capillarity

This paper investigates the isentropic compressible Euler–Korteweg system with a density-dependent capillary coefficient. Assuming the initial density is compactly supported and the radius of its support grows at most polynomially in time (i.e., $R(t) \leq C_{1}(1+t)^{\alpha}$ with $\alpha < 1$ ), we prove that smooth solutions must blow up in finite time and establish an explicit upper bound for the blow-up time.

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Publication Details

Journal
Boundary Value Problems
Published
2025-11-21
DOI
https://doi.org/10.1186/s13661-025-02160-1
Primary Topic
Navier-Stokes equation solutions
Type
article
Field-Weighted Citation Impact
0.00

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article

Finite-time blow-up for the compressible Euler–Korteweg system with density-dependent capillarity

Jianwei Yang, Xiaoxia Yang
Boundary Value Problems
Navier-Stokes equation solutions
article

Finite-time blow-up for the compressible Euler–Korteweg system with density-dependent capillarity

Jianwei Yang, Xiaoxia Yang
article en

Abstract

This paper investigates the isentropic compressible Euler–Korteweg system with a density-dependent capillary coefficient. Assuming the initial density is compactly supported and the radius of its support grows at most polynomially in time (i.e., $R(t) \leq C_{1}(1+t)^{\alpha}$ with $\alpha < 1$ ), we prove that smooth solutions must blow up in finite time and establish an explicit upper bound for the blow-up time.

Boundary Value ProblemsVol. 2025(1)
North China University of Water Resources and Electric Power (CN), Beijing University of Technology (CN), Beijing Information Science & Technology University (CN), University of Science and Technology Beijing (CN)
National Natural Science Foundation of China, Natural Science Foundation of Henan Province
Openalex Percentile: Top 51%
Navier-Stokes equation solutions
DOIOpen Access PDFOpenAlex
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Finite-time blow-up for the compressible Euler–Korteweg system with density-dependent capillarity — Jianwei Yang, Xiaoxia Yang · Boundary Value Problems (2025) | TGRS Research Map | TGRS