Chen, Qionglei; Nie, Yao; Ye, Weikui Sharp ill-posedness for the non-resistive MHD equations in Sobolev spaces. (English) Zbl 07797701 J. Funct. Anal. 286, No. 6, Article ID 110302, 22 p. (2024). MSC: 35Q35 76W05 76D05 35R25 35A01 35A02 46E35 PDFBibTeX XMLCite \textit{Q. Chen} et al., J. Funct. Anal. 286, No. 6, Article ID 110302, 22 p. (2024; Zbl 07797701) Full Text: DOI
Li, Zhouyu; Liu, Pan Regularity criteria for the 3D axisymmetric non-resistive MHD system in the swirl component of the vorticity. (English) Zbl 07784108 J. Geom. Anal. 34, No. 2, Paper No. 37, 22 p. (2024). MSC: 35Q35 76W05 35B65 35B07 PDFBibTeX XMLCite \textit{Z. Li} and \textit{P. Liu}, J. Geom. Anal. 34, No. 2, Paper No. 37, 22 p. (2024; Zbl 07784108) Full Text: DOI
Wu, Jiahong; Zhai, Xiaoping Global small solutions to the 3D compressible viscous non-resistive MHD system. (English) Zbl 1527.35305 Math. Models Methods Appl. Sci. 33, No. 13, 2629-2656 (2023). MSC: 35Q35 35A01 35A02 76W05 PDFBibTeX XMLCite \textit{J. Wu} and \textit{X. Zhai}, Math. Models Methods Appl. Sci. 33, No. 13, 2629--2656 (2023; Zbl 1527.35305) Full Text: DOI arXiv
Chen, Tiantian; Lin, Hongxia; Wu, Jiahong The 2D magnetohydrodynamic system with Euler-like velocity equation and partial magnetic diffusion. (English) Zbl 07778770 Stud. Appl. Math. 150, No. 3, 629-649 (2023). MSC: 35Q31 76W05 76B03 76E25 35B35 35B20 35A01 35A02 PDFBibTeX XMLCite \textit{T. Chen} et al., Stud. Appl. Math. 150, No. 3, 629--649 (2023; Zbl 07778770) Full Text: DOI
Zheng, Yiming; Zhu, Yi Stability of 2D inviscid MHD equations with only vertical magnetic diffusion on \(\mathbb{T}^2\). (English) Zbl 07774842 J. Math. Phys. 64, No. 11, Article ID 111508, 11 p. (2023). MSC: 76W05 76B03 35Q35 PDFBibTeX XMLCite \textit{Y. Zheng} and \textit{Y. Zhu}, J. Math. Phys. 64, No. 11, Article ID 111508, 11 p. (2023; Zbl 07774842) Full Text: DOI
Zhai, Xiaoping Stability for the 2D incompressible MHD equations with only magnetic diffusion. (English) Zbl 07748175 J. Differ. Equations 374, 267-278 (2023). MSC: 35Q35 76W05 76E25 76D03 35B20 35B65 35A01 35A02 35R07 PDFBibTeX XMLCite \textit{X. Zhai}, J. Differ. Equations 374, 267--278 (2023; Zbl 07748175) Full Text: DOI arXiv
Gao, Song; Li, Shengxin; Wang, Jing Vanishing dissipation limit of solutions to initial boundary value problem for three dimensional incompressible magneto-hydrodynamic equations with transverse magnetic field. (English) Zbl 07748168 J. Differ. Equations 374, 29-55 (2023). MSC: 35Q35 76W05 76D03 35A01 35A02 35B65 PDFBibTeX XMLCite \textit{S. Gao} et al., J. Differ. Equations 374, 29--55 (2023; Zbl 07748168) Full Text: DOI
Li, Zhouyu Regularity criteria for the 3D axisymmetric non-resistive MHD system. (English) Zbl 1518.35553 Commun. Nonlinear Sci. Numer. Simul. 125, Article ID 107367, 14 p. (2023). MSC: 35Q35 76W05 35B65 PDFBibTeX XMLCite \textit{Z. Li}, Commun. Nonlinear Sci. Numer. Simul. 125, Article ID 107367, 14 p. (2023; Zbl 1518.35553) Full Text: DOI
Feng, Wen; Hafeez, Farzana; Wu, Jiahong; Regmi, Dipendra Stability and exponential decay for magnetohydrodynamic equations. (English) Zbl 1518.35093 Proc. R. Soc. Edinb., Sect. A, Math. 153, No. 3, 853-880 (2023). MSC: 35B40 35B35 35Q35 76D09 76W05 PDFBibTeX XMLCite \textit{W. Feng} et al., Proc. R. Soc. Edinb., Sect. A, Math. 153, No. 3, 853--880 (2023; Zbl 1518.35093) Full Text: DOI
Li, Yongsheng; Xu, Huan; Zhai, Xiaoping Global smooth solutions to the 3D compressible viscous non-isentropic magnetohydrodynamic flows without magnetic diffusion. (English) Zbl 1517.35182 J. Geom. Anal. 33, No. 8, Paper No. 246, 32 p. (2023). MSC: 35Q35 76N10 76W05 35B65 PDFBibTeX XMLCite \textit{Y. Li} et al., J. Geom. Anal. 33, No. 8, Paper No. 246, 32 p. (2023; Zbl 1517.35182) Full Text: DOI
Wang, Jinhuan; Tan, Wei; Nie, Yongsheng A regularity criterion for the 3D generalized MHD system involving partial components. (English) Zbl 1512.76145 J. Math. Phys. 64, No. 5, Article ID 051505, 10 p. (2023). MSC: 76W05 PDFBibTeX XMLCite \textit{J. Wang} et al., J. Math. Phys. 64, No. 5, Article ID 051505, 10 p. (2023; Zbl 1512.76145) Full Text: DOI
Li, Jinlu; Yin, Zhaoyang; Zhu, Weipeng Non-uniform continuous dependence and continuous dependence for the non-resistive MHD equations. (English) Zbl 07691796 Adv. Math. 426, Article ID 109112, 23 p. (2023). MSC: 76W05 35Q35 35Q60 PDFBibTeX XMLCite \textit{J. Li} et al., Adv. Math. 426, Article ID 109112, 23 p. (2023; Zbl 07691796) Full Text: DOI arXiv
Feng, Wen; Wang, Weinan; Wu, Jiahong Nonlinear stability for the 2D incompressible MHD system with fractional dissipation in the horizontal direction. (English) Zbl 1514.35348 J. Evol. Equ. 23, No. 2, Paper No. 32, 37 p. (2023). MSC: 35Q35 76W05 76E25 35B35 35B40 35B05 26A33 35R11 PDFBibTeX XMLCite \textit{W. Feng} et al., J. Evol. Equ. 23, No. 2, Paper No. 32, 37 p. (2023; Zbl 1514.35348) Full Text: DOI
Feng, Wen; Hafeez, Farzana; Wu, Jiahong Stabilizing effect of the magnetic field and large-time behavior of 2D incompressible MHD system with vertical dissipation. (English) Zbl 1514.35347 J. Math. Fluid Mech. 25, No. 2, Paper No. 33, 42 p. (2023). MSC: 35Q35 76W05 76E25 76D05 35B35 35B40 PDFBibTeX XMLCite \textit{W. Feng} et al., J. Math. Fluid Mech. 25, No. 2, Paper No. 33, 42 p. (2023; Zbl 1514.35347) Full Text: DOI
Wu, Xing; Li, Jinlu Global smooth solutions to the 3D generalized Hall-magnetohydrodynamic equations with large data. (English) Zbl 1509.35253 Appl. Anal. 102, No. 2, 542-551 (2023). MSC: 35Q35 76D03 PDFBibTeX XMLCite \textit{X. Wu} and \textit{J. Li}, Appl. Anal. 102, No. 2, 542--551 (2023; Zbl 1509.35253) Full Text: DOI
Aarach, Nacer; Zhu, Ning Global well-posedness of 3D homogeneous and inhomogeneous MHD system with small unidirectional derivative. (English) Zbl 1512.35432 Calc. Var. Partial Differ. Equ. 62, No. 4, Paper No. 117, 39 p. (2023). MSC: 35Q30 76D03 76W05 35A01 35A02 PDFBibTeX XMLCite \textit{N. Aarach} and \textit{N. Zhu}, Calc. Var. Partial Differ. Equ. 62, No. 4, Paper No. 117, 39 p. (2023; Zbl 1512.35432) Full Text: DOI
Li, Zhouyu; Liu, Wenjuan Regularity criteria for the 3D axisymmetric non-resistive MHD system in Lorentz spaces. (English) Zbl 1510.35238 Result. Math. 78, No. 3, Paper No. 86, 20 p. (2023). MSC: 35Q35 76W05 76D05 35B07 35B44 35B65 35D35 PDFBibTeX XMLCite \textit{Z. Li} and \textit{W. Liu}, Result. Math. 78, No. 3, Paper No. 86, 20 p. (2023; Zbl 1510.35238) Full Text: DOI
Feng, Weixun; Qin, Dongdong; Zhu, Rui; Chen, Zhi Global well-posedness for MHD equations with magnetic diffusion and damping term in \(\mathbb{R}^2\). (English) Zbl 1509.35216 J. Geom. Anal. 33, No. 4, Paper No. 131, 31 p. (2023). MSC: 35Q35 35A01 35A02 35B45 35B30 76W05 35Q79 35Q49 PDFBibTeX XMLCite \textit{W. Feng} et al., J. Geom. Anal. 33, No. 4, Paper No. 131, 31 p. (2023; Zbl 1509.35216) Full Text: DOI
Qiu, Hua; Yao, Zheng-an Local existence for the non-resistive magnetohydrodynamic system with fractional dissipation in the \(L^p\) framework. (English) Zbl 1503.35181 SN Partial Differ. Equ. Appl. 3, No. 6, Paper No. 73, 38 p. (2022). MSC: 35Q35 76W05 76D03 35A01 35A02 35D30 26A33 35R11 PDFBibTeX XMLCite \textit{H. Qiu} and \textit{Z.-a. Yao}, SN Partial Differ. Equ. Appl. 3, No. 6, Paper No. 73, 38 p. (2022; Zbl 1503.35181) Full Text: DOI
Chen, Zhi; Feng, Weixun; Qin, Dongdong Stability for the 2D MHD equations with horizontal dissipation. (English) Zbl 1500.35234 Asymptotic Anal. 129, No. 3-4, 361-377 (2022). MSC: 35Q35 76W05 76E25 35B35 PDFBibTeX XMLCite \textit{Z. Chen} et al., Asymptotic Anal. 129, No. 3--4, 361--377 (2022; Zbl 1500.35234) Full Text: DOI
Ye, Wei Kui; Yin, Zhao Yang Global well-posedness for the non-viscous MHD equations with magnetic diffusion in critical Besov spaces. (English) Zbl 1498.35451 Acta Math. Sin., Engl. Ser. 38, No. 9, 1493-1511 (2022). MSC: 35Q35 35B30 35B44 35D30 76W05 35B65 35A01 35A02 42B25 PDFBibTeX XMLCite \textit{W. K. Ye} and \textit{Z. Y. Yin}, Acta Math. Sin., Engl. Ser. 38, No. 9, 1493--1511 (2022; Zbl 1498.35451) Full Text: DOI arXiv
Lai, Suhua; Wu, Jiahong; Zhang, Jianwen Stabilizing effect of magnetic field on the 2D ideal magnetohydrodynamic flow with mixed partial damping. (English) Zbl 1506.35165 Calc. Var. Partial Differ. Equ. 61, No. 4, Paper No. 126, 31 p. (2022). MSC: 35Q35 35Q31 76W05 35A01 35B35 35B65 76B03 76E25 PDFBibTeX XMLCite \textit{S. Lai} et al., Calc. Var. Partial Differ. Equ. 61, No. 4, Paper No. 126, 31 p. (2022; Zbl 1506.35165) Full Text: DOI
Yan, Weiping; Rădulescu, Vicenţiu D. The inviscid limit for the incompressible stationary magnetohydrodynamics equations in three dimensions. (English) Zbl 1492.76155 Bull. Math. Sci. 12, No. 1, Article ID 2150006, 37 p. (2022). Reviewer: Stephen Wollman (New York) MSC: 76W05 35Q35 35Q60 PDFBibTeX XMLCite \textit{W. Yan} and \textit{V. D. Rădulescu}, Bull. Math. Sci. 12, No. 1, Article ID 2150006, 37 p. (2022; Zbl 1492.76155) Full Text: DOI
Zhang, Zhaoyun Global regularity of the 2D generalized MHD equations with velocity damping and Laplacian magnetic diffusion. (English) Zbl 1490.35362 Z. Angew. Math. Phys. 73, No. 2, Paper No. 63, 16 p. (2022). MSC: 35Q35 76W05 35B65 PDFBibTeX XMLCite \textit{Z. Zhang}, Z. Angew. Math. Phys. 73, No. 2, Paper No. 63, 16 p. (2022; Zbl 1490.35362) Full Text: DOI
Jia, Yan; Xie, Qianqian; Dong, Bo-Qing Global regularity of the 3D magneto-micropolar equations with fractional dissipation. (English) Zbl 1479.35669 Z. Angew. Math. Phys. 73, No. 1, Paper No. 19, 15 p. (2022). MSC: 35Q35 35B65 35B45 76A10 76B03 76W05 26A33 35R11 PDFBibTeX XMLCite \textit{Y. Jia} et al., Z. Angew. Math. Phys. 73, No. 1, Paper No. 19, 15 p. (2022; Zbl 1479.35669) Full Text: DOI
Liu, Cheng-Jie; Xie, Feng; Yang, Tong Uniform regularity and vanishing viscosity limit for the incompressible non-resistive MHD system with TMF. (English) Zbl 1504.35350 Commun. Pure Appl. Anal. 20, No. 7-8, 2725-2750 (2021). MSC: 35Q35 35M31 35B65 76W05 76N20 PDFBibTeX XMLCite \textit{C.-J. Liu} et al., Commun. Pure Appl. Anal. 20, No. 7--8, 2725--2750 (2021; Zbl 1504.35350) Full Text: DOI
Paicu, Marius; Zhu, Ning Global regularity for the 2D MHD and tropical climate model with horizontal dissipation. (English) Zbl 1525.35201 J. Nonlinear Sci. 31, No. 6, Paper No. 99, 39 p. (2021). MSC: 35Q35 35B40 35B45 35B65 35A01 35A02 35A09 42B25 76D03 76W05 86A08 PDFBibTeX XMLCite \textit{M. Paicu} and \textit{N. Zhu}, J. Nonlinear Sci. 31, No. 6, Paper No. 99, 39 p. (2021; Zbl 1525.35201) Full Text: DOI arXiv
Yan, Weiping Asymptotic stability of explicit blowup solutions for three-dimensional incompressible magnetohydrodynamics equations. (English) Zbl 1478.35044 J. Geom. Anal. 31, No. 12, 12053-12097 (2021). MSC: 35B40 35A21 35B35 35B44 35Q35 76W05 PDFBibTeX XMLCite \textit{W. Yan}, J. Geom. Anal. 31, No. 12, 12053--12097 (2021; Zbl 1478.35044) Full Text: DOI arXiv
Li, Jinlu; Yu, Yanghai Global smooth solutions of the generalized MHD equations with large initial data. (English) Zbl 1473.35446 Result. Math. 76, No. 2, Paper No. 61, 14 p. (2021). MSC: 35Q35 76D03 76W05 35B65 35A02 26A33 35R11 PDFBibTeX XMLCite \textit{J. Li} and \textit{Y. Yu}, Result. Math. 76, No. 2, Paper No. 61, 14 p. (2021; Zbl 1473.35446) Full Text: DOI arXiv
Feng, Wen; Hafeez, Farzana; Wu, Jiahong Influence of a background magnetic field on a 2D magnetohydrodynamic flow. (English) Zbl 1466.35295 Nonlinearity 34, No. 4, 2527-2562 (2021). MSC: 35Q35 35A01 35B35 76W05 76D05 76D09 PDFBibTeX XMLCite \textit{W. Feng} et al., Nonlinearity 34, No. 4, 2527--2562 (2021; Zbl 1466.35295) Full Text: DOI
Yan, Weiping; Rădulescu, Vicenţiu D. Global small finite energy solutions for the incompressible magnetohydrodynamics equations in \(\mathbb{R}^+ \times \mathbb{R}^2\). (English) Zbl 1470.76117 J. Differ. Equations 277, 114-152 (2021). Reviewer: Yongzhong Sun (Nanjing) MSC: 76W05 76N10 35Q35 PDFBibTeX XMLCite \textit{W. Yan} and \textit{V. D. Rădulescu}, J. Differ. Equations 277, 114--152 (2021; Zbl 1470.76117) Full Text: DOI
Li, Chaoying; Wu, Jiahong; Xu, Xiaojing Smoothing and stabilization effects of magnetic field on electrically conducting fluids. (English) Zbl 1458.35339 J. Differ. Equations 276, 368-403 (2021). MSC: 35Q35 35B35 76W05 35B40 76E25 PDFBibTeX XMLCite \textit{C. Li} et al., J. Differ. Equations 276, 368--403 (2021; Zbl 1458.35339) Full Text: DOI
Dai, Yichen; Ji, Ruihong; Wu, Jiahong Unique weak solutions of the magnetohydrodynamic equations with fractional dissipation. (English) Zbl 07809736 ZAMM, Z. Angew. Math. Mech. 100, No. 7, Article ID e201900290, 20 p. (2020). MSC: 35Qxx 76Wxx 35Bxx PDFBibTeX XMLCite \textit{Y. Dai} et al., ZAMM, Z. Angew. Math. Mech. 100, No. 7, Article ID e201900290, 20 p. (2020; Zbl 07809736) Full Text: DOI
Ye, Hailong; Jia, Yan; Dong, Bo-Qing Sharp time decay rates of \(H^{1}\) weak solutions for the 2D MHD equations with linear damping velocity. (English) Zbl 1451.35027 Nonlinearity 33, No. 9, 4857-4877 (2020). MSC: 35B40 35D30 35Q35 76W05 PDFBibTeX XMLCite \textit{H. Ye} et al., Nonlinearity 33, No. 9, 4857--4877 (2020; Zbl 1451.35027) Full Text: DOI
Boardman, Nicki; Lin, Hongxia; Wu, Jiahong Stabilization of a background magnetic field on a 2 dimensional magnetohydrodynamic flow. (English) Zbl 1450.35210 SIAM J. Math. Anal. 52, No. 5, 5001-5035 (2020). MSC: 35Q35 76D03 76W05 35B35 PDFBibTeX XMLCite \textit{N. Boardman} et al., SIAM J. Math. Anal. 52, No. 5, 5001--5035 (2020; Zbl 1450.35210) Full Text: DOI
Faraco, Daniel; Lindberg, Sauli Proof of Taylor’s conjecture on magnetic helicity conservation. (English) Zbl 1433.35269 Commun. Math. Phys. 373, No. 2, 707-738 (2020). MSC: 35Q35 76W05 76D05 82D10 78A25 PDFBibTeX XMLCite \textit{D. Faraco} and \textit{S. Lindberg}, Commun. Math. Phys. 373, No. 2, 707--738 (2020; Zbl 1433.35269) Full Text: DOI arXiv
Li, Jinlu; Zhai, Xiaoping; Yin, Zhaoyang On the global well-posedness of the tropical climate model. (English) Zbl 07783389 ZAMM, Z. Angew. Math. Mech. 99, No. 6, Article ID e201700306, 17 p. (2019). MSC: 35Q35 35Q30 76N10 86A10 76D03 86A08 PDFBibTeX XMLCite \textit{J. Li} et al., ZAMM, Z. Angew. Math. Mech. 99, No. 6, Article ID e201700306, 17 p. (2019; Zbl 07783389) Full Text: DOI
Dai, Yichen; Tan, Zhong; Wu, Jiahong A class of global large solutions to the magnetohydrodynamic equations with fractional dissipation. (English) Zbl 1428.35353 Z. Angew. Math. Phys. 70, No. 5, Paper No. 153, 13 p. (2019). MSC: 35Q35 76D03 76W05 35R11 35B65 35A01 35A02 PDFBibTeX XMLCite \textit{Y. Dai} et al., Z. Angew. Math. Phys. 70, No. 5, Paper No. 153, 13 p. (2019; Zbl 1428.35353) Full Text: DOI
Li, Jinlu; Yang, Minghua; Yu, Yanghai A class large solution of the 2D MHD equations with velocity and magnetic damping. (English) Zbl 1414.76091 J. Math. Phys. 60, No. 3, 031503, 6 p. (2019). MSC: 76W05 PDFBibTeX XMLCite \textit{J. Li} et al., J. Math. Phys. 60, No. 3, 031503, 6 p. (2019; Zbl 1414.76091) Full Text: DOI arXiv