Incompressible Euler equations in 3D bounded domains in a critical space
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arXiv
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| Format: | Preprint |
| Publié: |
2026
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| _version_ | 1866914488056283136 |
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| author | Iwabuchi, Tsukasa Kozono, Hideo |
| author_facet | Iwabuchi, Tsukasa Kozono, Hideo |
| contents | We consider the 3D incompressible Euler equations in bounded domains $Ω$ with smooth boundary $\partialΩ$. Based on the paper by Iwabuchi, Matsuyama and Taniguchi (2019), we define the Besov space $B^s_{p, q}(A)$ by means of the Stokes operator $A$ with the Neumann boundary condition on $\partialΩ$, and prove unique local existence theorem of strong solution for the initial data in the critical Besov space $B^{\frac52}_{2, 1}(A)$. Our proof relies on the method of vanishing viscosity. The commutator estimate plays an essential role for derivation of energy bounds which hold uniformly with respect to viscosity constants. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_28070 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Incompressible Euler equations in 3D bounded domains in a critical space Iwabuchi, Tsukasa Kozono, Hideo Analysis of PDEs 35Q35, 35Q86 We consider the 3D incompressible Euler equations in bounded domains $Ω$ with smooth boundary $\partialΩ$. Based on the paper by Iwabuchi, Matsuyama and Taniguchi (2019), we define the Besov space $B^s_{p, q}(A)$ by means of the Stokes operator $A$ with the Neumann boundary condition on $\partialΩ$, and prove unique local existence theorem of strong solution for the initial data in the critical Besov space $B^{\frac52}_{2, 1}(A)$. Our proof relies on the method of vanishing viscosity. The commutator estimate plays an essential role for derivation of energy bounds which hold uniformly with respect to viscosity constants. |
| title | Incompressible Euler equations in 3D bounded domains in a critical space |
| topic | Analysis of PDEs 35Q35, 35Q86 |
| url | https://arxiv.org/abs/2603.28070 |