Salvato in:
| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| Soggetti: | |
| Accesso online: | https://arxiv.org/abs/2301.01399 |
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Sommario:
- We consider the three-dimensional incompressible Euler equation \begin{equation*}\left\{\begin{aligned} &\partial_t Ω+U \cdot \nabla Ω+Ω\cdot \nabla U=0 \\ &Ω(x,0)=Ω_0(x) \end{aligned}\right. \end{equation*} in the whole space $\mathbb{R}^3$. Under the assumption that the initial velocity is helical and without swirl, we prove the global well-posedness of weak solutions in $L^1_1 \bigcap L^{\infty}_1(\mathbb{R}^3)$. The vortex transport formula is also obtained in our article.