Global well-posedness of 3-D density-dependent incompressible MHD equations with variable resistivity
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916638805196800 |
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| author | Abidi, Hammadi Gui, Guilong Zhang, Ping |
| author_facet | Abidi, Hammadi Gui, Guilong Zhang, Ping |
| contents | In this paper, we investigate the global existence of weak solutions to 3-D inhomogeneous incompressible MHD equations with variable viscosity and resistivity, which is sufficiently close to $1$ in $L^\infty(\mathbb{R}^3),$ provided that the initial density is bounded from above and below by positive constants, and both the initial velocity and magnetic field are small enough in the critical space $\dot{H}^{\frac{1}{2}}(\mathbb{R}^3).$ Furthermore, if we assume in addition that the kinematic viscosity equals $1,$ and both the initial velocity and magnetic field belong to $\dot{B}^{\frac{1}{2}}_{2,1}(\mathbb{R}^3),$ we can also prove the uniqueness of such solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_00700 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global well-posedness of 3-D density-dependent incompressible MHD equations with variable resistivity Abidi, Hammadi Gui, Guilong Zhang, Ping Analysis of PDEs 35Q30, 76D03 In this paper, we investigate the global existence of weak solutions to 3-D inhomogeneous incompressible MHD equations with variable viscosity and resistivity, which is sufficiently close to $1$ in $L^\infty(\mathbb{R}^3),$ provided that the initial density is bounded from above and below by positive constants, and both the initial velocity and magnetic field are small enough in the critical space $\dot{H}^{\frac{1}{2}}(\mathbb{R}^3).$ Furthermore, if we assume in addition that the kinematic viscosity equals $1,$ and both the initial velocity and magnetic field belong to $\dot{B}^{\frac{1}{2}}_{2,1}(\mathbb{R}^3),$ we can also prove the uniqueness of such solution. |
| title | Global well-posedness of 3-D density-dependent incompressible MHD equations with variable resistivity |
| topic | Analysis of PDEs 35Q30, 76D03 |
| url | https://arxiv.org/abs/2503.00700 |