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

Corentin Audiard

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arXiv · 1906.01385

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

Corentin Audiard

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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.

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Corentin Audiard. 2019-06-04. On the time of existence of solutions of the Euler-Korteweg system. https://arxiv.org/abs/1906.01385

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