Asymptotic stability for the 3D Navier-Stokes equations in $L^3$ and nearby spaces
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| Format: | Preprint |
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2024
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| _version_ | 1866914952844935168 |
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| author | Bradshaw, Zachary Wang, Weinan |
| author_facet | Bradshaw, Zachary Wang, Weinan |
| contents | We provide a short proof of $L^3$-asymptotic stability around vector fields that are small in weak-$L^3$, including small Landau solutions. We show that asymptotic stability also holds for vector fields in the range of Lorentz spaces strictly between $L^3$ and weak-$L^3$, as well as in the closure of the test functions in weak-$L^3$. To provide a comprehensive perspective on the matter, we observe that asymptotic stability of Landau solutions does not generally extend to weak-$L^3$ via a counterexample. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2409_12918 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Asymptotic stability for the 3D Navier-Stokes equations in $L^3$ and nearby spaces Bradshaw, Zachary Wang, Weinan Analysis of PDEs We provide a short proof of $L^3$-asymptotic stability around vector fields that are small in weak-$L^3$, including small Landau solutions. We show that asymptotic stability also holds for vector fields in the range of Lorentz spaces strictly between $L^3$ and weak-$L^3$, as well as in the closure of the test functions in weak-$L^3$. To provide a comprehensive perspective on the matter, we observe that asymptotic stability of Landau solutions does not generally extend to weak-$L^3$ via a counterexample. |
| title | Asymptotic stability for the 3D Navier-Stokes equations in $L^3$ and nearby spaces |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2409.12918 |