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Lower bounds for the lifespan of solutions to the Euler--Korteweg equations

  • Haruhiro Kurabe
  • Ryo Takada
  • Tomoaki Yoshizawa
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Abstract

We consider the initial value problem for the Euler--Korteweg equations in the class of irrotational flows. In every space dimension d geqslant 2, we establish a quantitative lower bound for the lifespan of solutions that explicitly exhibits its dependence on the Weber number, the Mach number, and the Sobolev norm of the initial perturbation. In particular, this lower bound can be taken arbitrarily large in a low-Weber-number regime under a suitable algebraic relation between the Mach and Weber numbers.

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Cite

BibTeXRIS
BibTeX
@misc{kurabe2026lower,
  title = {{Lower bounds for the lifespan of solutions to the Euler--Korteweg equations}},
  author = {Haruhiro Kurabe and Ryo Takada and Tomoaki Yoshizawa},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.21244},
  eprint = {2609.21244},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.21244},
}
RIS
TY  - UNPB
TI  - Lower bounds for the lifespan of solutions to the Euler--Korteweg equations
AU  - Haruhiro Kurabe
AU  - Ryo Takada
AU  - Tomoaki Yoshizawa
PY  - 2026
DA  - 2026/09/18
PB  - arXiv
DO  - 10.48550/arxiv.2609.21244
UR  - https://arxiv.org/abs/2609.21244
AB  - We consider the initial value problem for the Euler--Korteweg equations in the class of irrotational flows. In every space dimension d geqslant 2, we establish a quantitative lower bound for the lifespan of solutions that explicitly exhibits its dependence on the Weber number, the Mach number, and the Sobolev norm of the initial perturbation. In particular, this lower bound can be taken arbitrarily large in a low-Weber-number regime under a suitable algebraic relation between the Mach and Weber numbers.
ER  -