Work

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

Year: 2025

Type: article

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.

Source: Boundary Value Problems

DOI: 10.1186/s13661-025-02160-1

Authors: Xiaoxia Yang, Jianwei Yang

Institutions: Beijing University of Technology, North China University of Water Resources and Electric Power

Language: English

Topic: Navier-Stokes equation solutions

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $1,890

Funders: National Natural Science Foundation of China, Natural Science Foundation of Henan Province