Infinite norm of the derivative of the solution operator of Euler equations
Fuente:
arXiv
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| Autor principal: | |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866916291063840768 |
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| author | Li, Y. Charles |
| author_facet | Li, Y. Charles |
| contents | Through a simple and elegant argument, we prove that the norm of the derivative of the solution operator of Euler equations posed in the Sobolev space $H^n$, along any base solution that is in $H^n$ but not in $H^{n+1}$, is infinite. We also review the counterpart of this result for Navier-Stokes equations at high Reynolds number from the perspective of fully developed turbulence. Finally we present a few examples and numerical simulations to show a more complete picture of the so-called rough dependence upon initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2009_03967 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Infinite norm of the derivative of the solution operator of Euler equations Li, Y. Charles Analysis of PDEs Mathematical Physics Chaotic Dynamics Atmospheric and Oceanic Physics Fluid Dynamics Through a simple and elegant argument, we prove that the norm of the derivative of the solution operator of Euler equations posed in the Sobolev space $H^n$, along any base solution that is in $H^n$ but not in $H^{n+1}$, is infinite. We also review the counterpart of this result for Navier-Stokes equations at high Reynolds number from the perspective of fully developed turbulence. Finally we present a few examples and numerical simulations to show a more complete picture of the so-called rough dependence upon initial data. |
| title | Infinite norm of the derivative of the solution operator of Euler equations |
| topic | Analysis of PDEs Mathematical Physics Chaotic Dynamics Atmospheric and Oceanic Physics Fluid Dynamics |
| url | https://arxiv.org/abs/2009.03967 |