Uniform Boundedness of Homogeneous Incompressible Flows in $\mathbb{R}^3$
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arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866915185962254336 |
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| author | Iotti, Ulisse |
| author_facet | Iotti, Ulisse |
| contents | This paper investigates the extendability of local solutions for incompressible 3D Navier-Stokes and 3D Euler problems, with initial data $\mathbf{u}_0$ in the Sobolev space $H^s (\mathbb{R}^3)$, where $s$ ensures the existence and uniqueness of classical solutions. A geometric decomposition of the configuration space, identified by the orthogonality between the solution $\mathbf{u}$ and the pressure forces $\nabla p$, splits the problem into two simpler subproblems, which enable the uniform boundedness of the solution in each component of the partition, thereby ensuring the extendability of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_03991 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniform Boundedness of Homogeneous Incompressible Flows in $\mathbb{R}^3$ Iotti, Ulisse Analysis of PDEs Numerical Analysis Mathematical Physics Dynamical Systems This paper investigates the extendability of local solutions for incompressible 3D Navier-Stokes and 3D Euler problems, with initial data $\mathbf{u}_0$ in the Sobolev space $H^s (\mathbb{R}^3)$, where $s$ ensures the existence and uniqueness of classical solutions. A geometric decomposition of the configuration space, identified by the orthogonality between the solution $\mathbf{u}$ and the pressure forces $\nabla p$, splits the problem into two simpler subproblems, which enable the uniform boundedness of the solution in each component of the partition, thereby ensuring the extendability of the solution. |
| title | Uniform Boundedness of Homogeneous Incompressible Flows in $\mathbb{R}^3$ |
| topic | Analysis of PDEs Numerical Analysis Mathematical Physics Dynamical Systems |
| url | https://arxiv.org/abs/2503.03991 |