Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866917588367310848 |
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| author | Hofmanová, Martina Pappalettera, Umberto Zhu, Rongchan Zhu, Xiangchan |
| author_facet | Hofmanová, Martina Pappalettera, Umberto Zhu, Rongchan Zhu, Xiangchan |
| contents | We propose a novel approach to induce anomalous dissipation through advection driven by turbulent fluid flows. Specifically, we establish the existence of a velocity field $v$ satisfying randomly forced Navier-Stokes equations, leading to total dissipation of kinetic energy in finite time when advecting a passive scalar. This dissipation phenomenon is uniform across viscosity parameters and initial conditions, representing a case of anomalous dissipation. We further explore dissipation induced by individual realizations of $v$. Our results extend to scenarios where the passive scalar is replaced by solutions to two or three-dimensional deterministic Navier-Stokes equations advected by $v$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2305_08090 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations Hofmanová, Martina Pappalettera, Umberto Zhu, Rongchan Zhu, Xiangchan Analysis of PDEs Probability We propose a novel approach to induce anomalous dissipation through advection driven by turbulent fluid flows. Specifically, we establish the existence of a velocity field $v$ satisfying randomly forced Navier-Stokes equations, leading to total dissipation of kinetic energy in finite time when advecting a passive scalar. This dissipation phenomenon is uniform across viscosity parameters and initial conditions, representing a case of anomalous dissipation. We further explore dissipation induced by individual realizations of $v$. Our results extend to scenarios where the passive scalar is replaced by solutions to two or three-dimensional deterministic Navier-Stokes equations advected by $v$. |
| title | Anomalous and total dissipation due to advection by solutions of randomly forced Navier-Stokes equations |
| topic | Analysis of PDEs Probability |
| url | https://arxiv.org/abs/2305.08090 |