On the time of existence of solutions of the Euler-Korteweg system

2019/06/04 by Corentin Audiard, Audiard, Corentin · 1 citation
Engineering · Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1906.01385

openalex publication_date 2019/06/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Under a natural stability condition on the pressure, it is known that for small irrotational initial data, the solutions of the Euler-Korteweg system are global in time. When the initial velocity has a small rotational part, we obtain a lower bound on the time of existence that depends only on the rotational part. In the zero vorticity limit we recover the previous global well-posedness result. Independently of this analysis, we also provide (in a special case) a simple example of solution that blows up in finite time.

Citations

• Global solutions for the gravity water waves equation in dimension 3

Cited by

• The zero capillarity limit for the Euler-Korteweg system with no-flux boundary conditions

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