Well-posedness for 2D non-homogeneous incompressible fluids with general density-dependent odd viscosity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866910224150953984 |
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| author | Pageard, Matthieu |
| author_facet | Pageard, Matthieu |
| contents | We study the initial value problem for a system of equations describing the motion of two-dimensional non-homogeneous incompressible fluids exhibiting odd (non-dissipative) viscosity effects. We consider the complete odd viscous stress tensor with a general density-dependent viscosity coefficient $f(ρ)$. Under suitable assumptions, we prove the local existence and uniqueness of strong solutions in $H^s(\mathbb{R}^2)$ $(s>2)$, for a class of viscosity coefficients covering the particular case $f(ρ)=aρ^α+b$ for any $(a,b,α)\in\mathbb{R}^3$, generalising the result of Fanelli, Granero-Belinchón and Scrobogna, devoted to the case $f(ρ)=ρ$. Additionally, we are able to do so without requiring the initial density variation to belong to $L^2(\mathbb{R}^2)$. As a major step of the proof, we exhibit an effective velocity for this sytem, generalising the so-called "Elsässer formulation" recently derived by Fanelli and Vasseur. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2511_02948 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Well-posedness for 2D non-homogeneous incompressible fluids with general density-dependent odd viscosity Pageard, Matthieu Analysis of PDEs 35Q35 (primary), 35B65, 76B03, 76D09 (secondary) We study the initial value problem for a system of equations describing the motion of two-dimensional non-homogeneous incompressible fluids exhibiting odd (non-dissipative) viscosity effects. We consider the complete odd viscous stress tensor with a general density-dependent viscosity coefficient $f(ρ)$. Under suitable assumptions, we prove the local existence and uniqueness of strong solutions in $H^s(\mathbb{R}^2)$ $(s>2)$, for a class of viscosity coefficients covering the particular case $f(ρ)=aρ^α+b$ for any $(a,b,α)\in\mathbb{R}^3$, generalising the result of Fanelli, Granero-Belinchón and Scrobogna, devoted to the case $f(ρ)=ρ$. Additionally, we are able to do so without requiring the initial density variation to belong to $L^2(\mathbb{R}^2)$. As a major step of the proof, we exhibit an effective velocity for this sytem, generalising the so-called "Elsässer formulation" recently derived by Fanelli and Vasseur. |
| title | Well-posedness for 2D non-homogeneous incompressible fluids with general density-dependent odd viscosity |
| topic | Analysis of PDEs 35Q35 (primary), 35B65, 76B03, 76D09 (secondary) |
| url | https://arxiv.org/abs/2511.02948 |