{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,10,9]],"date-time":"2025-10-09T00:42:44Z","timestamp":1759970564592,"version":"build-2065373602"},"reference-count":31,"publisher":"MDPI AG","issue":"2","license":[{"start":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T00:00:00Z","timestamp":1738022400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Natural Science Foundation of Shandong Province of China","award":["ZR2024MA033"],"award-info":[{"award-number":["ZR2024MA033"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>The objective of this paper is to analyze the asymptotic stability of global strong solutions to the boundary value problem of the compressible magnetohydrodynamic (MHD) equations for the ideal polytropic gas in which the viscosity \u03bb and heat conductivity \u03ba depend on temperature, i.e., \u03bb=\u03b8\u03b1 and \u03ba=\u03b8\u03b2 with \u03b1,\u03b2\u2208[0,+\u221e). Both the global-in-time existence and uniqueness of strong solutions are obtained under certain assumptions on the parameter \u03b1 and initial data. Moreover, based on accurate uniform-in-time estimates, we show that the global large solutions decay exponentially in time to the equilibrium states. Compared with the existing results, the initial data could be large if \u03b1 is small and the growth exponent \u03b2 can be arbitrarily large.<\/jats:p>","DOI":"10.3390\/axioms14020100","type":"journal-article","created":{"date-parts":[[2025,1,28]],"date-time":"2025-01-28T10:44:30Z","timestamp":1738061070000},"page":"100","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Asymptotic Stability of the Magnetohydrodynamic Flows with Temperature-Dependent Transport Coefficients"],"prefix":"10.3390","volume":"14","author":[{"given":"Mingyu","family":"Zhang","sequence":"first","affiliation":[{"name":"School of Mathematics and Statistics, Weifang University, Weifang 261061, China"}]}],"member":"1968","published-online":{"date-parts":[[2025,1,28]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"344","DOI":"10.1006\/jdeq.2001.4111","article-title":"Global solutions of nonlinear magnetohydrodynamics with large initial data","volume":"182","author":"Chen","year":"2002","journal-title":"J. Differ. Equ."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1424","DOI":"10.1137\/S0036139902409284","article-title":"Large solutions to the initial-boundary value problem for planar magnetohydrodynamics","volume":"63","author":"Wang","year":"2003","journal-title":"SIAM J. Math."},{"key":"ref_3","unstructured":"Chapman, S., and Colwing, T.G. (1990). The Mathematical Theory of Nonuniform Gases, Cambridge University Press. [3rd ed.]."},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"1323","DOI":"10.1002\/(SICI)1099-1476(199910)22:15<1323::AID-MMA80>3.0.CO;2-8","article-title":"A model of thermal dissipation for a one-dimensional viscous reactive and radiative","volume":"22","author":"Ducomet","year":"1999","journal-title":"Math. Methods Appl. Sci."},{"key":"ref_5","unstructured":"Antontsev, S.N., Kazhikhov, A.V., and Monakhov, V.N. (1990). Boundary Value Problems in Mechanics of Nonhomogeneous Fluids, Elsevier."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"157","DOI":"10.1006\/jdeq.1994.1064","article-title":"On initial boundary value problems for a viscous heat-conducting one-dimensional real gas","volume":"110","author":"Jiang","year":"1994","journal-title":"J. Differ. Equ."},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"76","DOI":"10.1016\/0022-0396(85)90023-3","article-title":"Global existence of large solutions to initial boundary value problems for the equations of one-dimensional motion of viscous polytropic gases","volume":"58","author":"Kawohl","year":"1985","journal-title":"J. Differ. Equ."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"273","DOI":"10.1016\/0021-8928(77)90011-9","article-title":"Unique global solutions with respect to time of the initial-boundary value problems for one-dimensional equations of a viscous gas","volume":"41","author":"Kazhikhov","year":"1977","journal-title":"J. Appl. Math. Mech."},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"1195","DOI":"10.1007\/s00205-015-0952-0","article-title":"Some uniform estimates and large-time behavior of solutions to one-dimensional compressible Navier-Stokes system in unbounded domain with large data","volume":"220","author":"Li","year":"2016","journal-title":"Arch. Ration. Mech. Anal."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"53","DOI":"10.1007\/BF03167901","article-title":"On the outer pressure problem of the one-dimensional polytropic ideal gas","volume":"5","author":"Nagasawa","year":"1988","journal-title":"Jpn. J. Appl. Math."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"413","DOI":"10.1016\/S0362-546X(99)00140-6","article-title":"Global existence and asymptotic behavior for a viscous heat-conducting one-dimensional real gas with fixed and thermally insulated endpoints","volume":"44","author":"Qin","year":"2001","journal-title":"Nonlinear Anal. TMA"},{"key":"ref_12","first-page":"317","article-title":"Sur la solubilit\u00e9 global des probl\u00e9mes monodimensionnels aux valeurs initinales-limit\u00e9s pour les \u00e9quations d\u2019un gaz visqueux et calorif\u00e9re","volume":"284","author":"Kazhikhov","year":"1977","journal-title":"C. R. Acad. Sci. Paris Ser. A"},{"key":"ref_13","first-page":"37","article-title":"To a theory of boundary value problems for equation of one-dimensional nonstationary motion of viscous heat-conduction gases","volume":"Volume 50","author":"Kazhikhov","year":"1981","journal-title":"Boundary Value Problems for Hydrodynamical Equations"},{"key":"ref_14","first-page":"825","article-title":"Global solutions to the initial value problem for the equation of one-dimensional motion of viscous polytropic gases","volume":"21","author":"Kawashima","year":"1981","journal-title":"J. Math. Kyoto Univ."},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"2237","DOI":"10.1142\/S0218202516500524","article-title":"One-dimensional compressible heat-conducting gas with temperature-dependent viscosity","volume":"26","author":"Wang","year":"2016","journal-title":"Math. Model. Methods Appl. Sci."},{"key":"ref_16","first-page":"721","article-title":"A model system of equations for the one-dimensional motion of a gas","volume":"4","year":"1968","journal-title":"Differ. Uravn."},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"676","DOI":"10.1016\/j.jde.2021.03.044","article-title":"Nonlinear exponential stability for the compressible Navier-Stokes equations with temperature-dependent transport coefficients","volume":"286","author":"Sun","year":"2021","journal-title":"J. Differ. Equ."},{"key":"ref_18","unstructured":"Cabannes, H. (1970). Theoretical Magnetofluiddynamics, Academic Press."},{"key":"ref_19","unstructured":"Landau, L.D., Lifshitz, E.M., and Pitaevskii, L.P. (1999). Electrodynamics of Continuous Media, Butterworth-Heinemann. [2nd ed.]."},{"key":"ref_20","unstructured":"Li, T.T., and Qin, T. (2005). Physics and Partial Differential Equations, Higher Education Press. [2nd ed.]. (In Chinese)."},{"key":"ref_21","doi-asserted-by":"crossref","unstructured":"Moreau, R. (1990). Magnetohydrodynamics, Klumer Academic Publishers.","DOI":"10.1007\/978-94-015-7883-7"},{"key":"ref_22","unstructured":"Polovin, R.V., and Demutskii, V.P. (1990). Fundamentals of Magnetohydrodynamics, Consultants Bureau."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"608","DOI":"10.1007\/s00033-003-1017-z","article-title":"Existence and continuous dependence of large solutions for the magnetohydrodynamics equations","volume":"54","author":"Chen","year":"2003","journal-title":"Z. Angew. Math. Phys."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"691","DOI":"10.1007\/s00220-006-0167-1","article-title":"Vanishing sheer viscosity limit in the magnetohydrodynamic equations","volume":"270","author":"Fan","year":"2007","journal-title":"Comm. Math. Phys."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"1853","DOI":"10.1016\/j.jde.2008.07.010","article-title":"Global solutions for a one-dimensional model problem in thermally radiative magnetohydrodynamics","volume":"245","author":"Zhang","year":"2008","journal-title":"J. Differ. Equ."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"1439","DOI":"10.1016\/j.jde.2012.05.003","article-title":"Global existence and exponential stability for a 1D compressible and radiative MHD flow","volume":"253","author":"Qin","year":"2012","journal-title":"J. Differ. Equ."},{"key":"ref_27","doi-asserted-by":"crossref","first-page":"3513","DOI":"10.1007\/s00208-024-02840-w","article-title":"Vanishing viscosity limit to the planar rarefaction wave with vacuum for 3-D full compressible Navier-Stokes equations with temperature-dependent transport coefficients","volume":"390","author":"Hou","year":"2024","journal-title":"Math. Ann."},{"key":"ref_28","doi-asserted-by":"crossref","first-page":"103979","DOI":"10.1016\/j.nonrwa.2023.103979","article-title":"Optimal control problems for the reaction- diffusion-convection equation with variable coefficients","volume":"75","author":"Baranovskii","year":"2024","journal-title":"Nonlin. Anal. RWA"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"2185","DOI":"10.1137\/130920617","article-title":"One-dimensional compressible Navier-Stokes equations with temperature dependent transport coefficients and large data","volume":"46","author":"Liu","year":"2014","journal-title":"SIAM J. Math. Anal."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"609","DOI":"10.1137\/0523031","article-title":"Global solutions to the compressible Navier-Stokes equations for a reacting mixture of nonlinear","volume":"23","author":"Chen","year":"1992","journal-title":"SIAM J. Math. Anal."},{"key":"ref_31","doi-asserted-by":"crossref","first-page":"193","DOI":"10.2977\/prims\/1195190106","article-title":"On the first initial-boundary value problem of compressible viscous fluid motion","volume":"13","author":"Tani","year":"1977","journal-title":"Publ. Res. Inst. Math. Sci."}],"container-title":["Axioms"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/100\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,8]],"date-time":"2025-10-08T10:37:54Z","timestamp":1759919874000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2075-1680\/14\/2\/100"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2025,1,28]]},"references-count":31,"journal-issue":{"issue":"2","published-online":{"date-parts":[[2025,2]]}},"alternative-id":["axioms14020100"],"URL":"https:\/\/doi.org\/10.3390\/axioms14020100","relation":{},"ISSN":["2075-1680"],"issn-type":[{"type":"electronic","value":"2075-1680"}],"subject":[],"published":{"date-parts":[[2025,1,28]]}}}