Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866929533928603648 |
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| author | Ciampa, Gennaro Crippa, Gianluca Spirito, Stefano |
| author_facet | Ciampa, Gennaro Crippa, Gianluca Spirito, Stefano |
| contents | The aim of this note is to study the Cauchy problem for the 2D Euler equations under very low regularity assumptions on the initial datum. We prove propagation of regularity of logarithmic order in the class of weak solutions with $L^p$ initial vorticity, provided that $p\geq 4$. We also study the inviscid limit from the 2D Navier-Stokes equations for vorticity with logarithmic regularity in the Yudovich class, showing a rate of convergence of order $|\logν|^{-α/2}$ with $α>0$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2402_07622 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations Ciampa, Gennaro Crippa, Gianluca Spirito, Stefano Analysis of PDEs 35Q30, 35Q31, 35Q35, 76B03 The aim of this note is to study the Cauchy problem for the 2D Euler equations under very low regularity assumptions on the initial datum. We prove propagation of regularity of logarithmic order in the class of weak solutions with $L^p$ initial vorticity, provided that $p\geq 4$. We also study the inviscid limit from the 2D Navier-Stokes equations for vorticity with logarithmic regularity in the Yudovich class, showing a rate of convergence of order $|\logν|^{-α/2}$ with $α>0$. |
| title | Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations |
| topic | Analysis of PDEs 35Q30, 35Q31, 35Q35, 76B03 |
| url | https://arxiv.org/abs/2402.07622 |