Volume 36, Issue 4
Global Well-Posedness for the 2-D MHD Equations with Magnetic Diffusion

Commun. Math. Res., 36 (2020), pp. 377-389.

Published online: 2020-11

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• Abstract

In this paper, we consider the 2-D MHD equations with magnetic resistivity but without dissipation on the torus. We prove that if the initial data is small in $H^4$($\mathbb{T}^2$), then the 2-D MHD equations are globally well-posed. To our knowledge, this is the first global well-posedness result for this system.

• Keywords

MHD equations, globally well-posedness.

35Q35, 35B30

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@Article{CMR-36-377, author = {Dongyi and Wei and and 9477 and and Dongyi Wei and Zhifei and Zhang and and 9478 and and Zhifei Zhang}, title = {Global Well-Posedness for the 2-D MHD Equations with Magnetic Diffusion}, journal = {Communications in Mathematical Research }, year = {2020}, volume = {36}, number = {4}, pages = {377--389}, abstract = {

In this paper, we consider the 2-D MHD equations with magnetic resistivity but without dissipation on the torus. We prove that if the initial data is small in $H^4$($\mathbb{T}^2$), then the 2-D MHD equations are globally well-posed. To our knowledge, this is the first global well-posedness result for this system.

}, issn = {2707-8523}, doi = {https://doi.org/10.4208/cmr.2020-0022}, url = {http://global-sci.org/intro/article_detail/cmr/18358.html} }
TY - JOUR T1 - Global Well-Posedness for the 2-D MHD Equations with Magnetic Diffusion AU - Wei , Dongyi AU - Zhang , Zhifei JO - Communications in Mathematical Research VL - 4 SP - 377 EP - 389 PY - 2020 DA - 2020/11 SN - 36 DO - http://doi.org/10.4208/cmr.2020-0022 UR - https://global-sci.org/intro/article_detail/cmr/18358.html KW - MHD equations, globally well-posedness. AB -

In this paper, we consider the 2-D MHD equations with magnetic resistivity but without dissipation on the torus. We prove that if the initial data is small in $H^4$($\mathbb{T}^2$), then the 2-D MHD equations are globally well-posed. To our knowledge, this is the first global well-posedness result for this system.

Dongyi Wei & Zhifei Zhang. (2020). Global Well-Posedness for the 2-D MHD Equations with Magnetic Diffusion. Communications in Mathematical Research . 36 (4). 377-389. doi:10.4208/cmr.2020-0022
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