{"@context":{"@vocab":"https://cir.nii.ac.jp/schema/1.0/","rdfs":"http://www.w3.org/2000/01/rdf-schema#","dc":"http://purl.org/dc/elements/1.1/","dcterms":"http://purl.org/dc/terms/","foaf":"http://xmlns.com/foaf/0.1/","prism":"http://prismstandard.org/namespaces/basic/2.0/","cinii":"http://ci.nii.ac.jp/ns/1.0/","datacite":"https://schema.datacite.org/meta/kernel-4/","ndl":"http://ndl.go.jp/dcndl/terms/","jpcoar":"https://github.com/JPCOAR/schema/blob/master/2.0/"},"@id":"https://cir.nii.ac.jp/crid/1390586444065083392.json","@type":"Article","productIdentifier":[{"identifier":{"@type":"DOI","@value":"10.2969/jmsj/92789278"}},{"identifier":{"@type":"NDL_BIB_ID","@value":"034225726"}},{"identifier":{"@type":"URI","@value":"http://id.ndl.go.jp/bib/034225726"}},{"identifier":{"@type":"URI","@value":"https://ndlsearch.ndl.go.jp/books/R000000004-I034225726"}}],"dc:title":[{"@language":"en","@value":"Compressible magnetohydrodynamics as a dissipative system"}],"dc:language":"en","description":[{"type":"abstract","notation":[{"@language":"en","@value":"<p>We consider the complete system of equations governing the motion of a general compressible, viscous, electrically and heat conductive fluid driven by non-conservative boundary conditions. We show the existence of a bounded absorbing set in the energy space and asymptotic compactness of trajectories. As a corollary, the set of all entire globally bounded solutions is identified as a natural attractor. Examples of boundary conditions giving rise to unbounded solutions are also discussed.</p>"}],"abstractLicenseFlag":"disallow"}],"creator":[{"@id":"https://cir.nii.ac.jp/crid/1410586444065083392","@type":"Researcher","foaf:name":[{"@language":"en","@value":"Březina Jan"}],"jpcoar:affiliationName":[{"@language":"en","@value":"Faculty of Arts and Science, Kyushu University"}]},{"@id":"https://cir.nii.ac.jp/crid/1410586444065083393","@type":"Researcher","foaf:name":[{"@language":"en","@value":"Feireisl Eduard"}],"jpcoar:affiliationName":[{"@language":"en","@value":"Institute of Mathematics of the Academy of Sciences of the Czech Republic"}]}],"publication":{"publicationIdentifier":[{"@type":"PISSN","@value":"00255645"},{"@type":"LISSN","@value":"00255645"},{"@type":"EISSN","@value":"18811167"},{"@type":"EISSN","@value":"18812333"},{"@type":"CODEN","@value":"NISUBC"},{"@type":"NDL_BIB_ID","@value":"000000118458"},{"@type":"ISSN","@value":"00255645"},{"@type":"NCID","@value":"AA0070177X"}],"prism:publicationName":[{"@language":"en","@value":"Journal of the Mathematical Society of Japan"},{"@language":"en","@value":"J. Math. Soc. Japan"},{"@language":"en","@value":"JMSJ, J. Math. Soc. Japan"},{"@language":"en","@value":"JMSJ"},{"@language":"ja","@value":"Ｊｏｕｒｎａｌ　ｏｆ　ｔｈｅ　Ｍａｔｈｅｍａｔｉｃａｌ　Ｓｏｃｉｅｔｙ　ｏｆ　Ｊａｐａｎ"},{"@language":"en","@value":"Journal of the Mathematical Society of Japan"}],"dc:publisher":[{"@language":"en","@value":"The Mathematical Society of Japan"},{"@language":"ja","@value":"一般社団法人 日本数学会"}],"prism:publicationDate":"2025","prism:volume":"77","prism:number":"3","prism:startingPage":"763","prism:endingPage":"795"},"reviewed":"false","url":[{"@id":"http://id.ndl.go.jp/bib/034225726"},{"@id":"https://ndlsearch.ndl.go.jp/books/R000000004-I034225726"}],"availableAt":"2025","foaf:topic":[{"@id":"https://cir.nii.ac.jp/all?q=compressible%20MHD%20system","dc:title":"compressible MHD system"},{"@id":"https://cir.nii.ac.jp/all?q=Levinson%20dissipativity","dc:title":"Levinson dissipativity"},{"@id":"https://cir.nii.ac.jp/all?q=asymptotic%20compactness","dc:title":"asymptotic compactness"},{"@id":"https://cir.nii.ac.jp/all?q=attractor","dc:title":"attractor"}],"relatedProduct":[{"@id":"https://cir.nii.ac.jp/crid/1360002219578761600","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"$L^r$-variational inequality for vector fields and the Helmholtz-Weyl decomposition in bounded domains"}]},{"@id":"https://cir.nii.ac.jp/crid/1360023718533372800","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Stellar Astrophysical Fluid Dynamics"}]},{"@id":"https://cir.nii.ac.jp/crid/1360023719100332800","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Astrophysical Fluid Dynamics"}]},{"@id":"https://cir.nii.ac.jp/crid/1360023720252933888","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Solvability of Control Problems for Stationary Equations of Magnetohydrodynamics of a Viscous Fluid"}]},{"@id":"https://cir.nii.ac.jp/crid/1360023721219112192","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"On the boundary conditions in estimating ∇ω by div ω and curl ω"}]},{"@id":"https://cir.nii.ac.jp/crid/1360283690249865856","@type":"Article","resourceType":"学術雑誌論文(journal article)","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Leray’s problem on the stationary Navier–Stokes equations with inhomogeneous boundary data"}]},{"@id":"https://cir.nii.ac.jp/crid/1360305191941780480","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"𝐿²-well-posedness of 3d div-curl boundary value problems"}]},{"@id":"https://cir.nii.ac.jp/crid/1360305192918531712","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The Rayleigh–Bénard Problem for Compressible Fluid Flows"}]},{"@id":"https://cir.nii.ac.jp/crid/1360305193247131264","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Towards Understanding Solar Convection and Activity (Invited Review)"}]},{"@id":"https://cir.nii.ac.jp/crid/1360305193348830336","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"On the Long-Time Behaviour of Solutions to the Navier–Stokes–Fourier System with a Time-Dependent Driving Force"}]},{"@id":"https://cir.nii.ac.jp/crid/1360305194309342848","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Explicit dimension estimates of attractors for the MHD equations in three-dimensional space"}]},{"@id":"https://cir.nii.ac.jp/crid/1360305194649538944","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The Maxwell Compactness Property in Bounded Weak Lipschitz Domains with Mixed Boundary Conditions"}]},{"@id":"https://cir.nii.ac.jp/crid/1360305194841496960","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"A Finite-Dimensional Attractor for Three-Dimensional Flow of Incompressible Fluids"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574095498872704","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Dynamics of Viscous Compressible Fluids"}]},{"@id":"https://cir.nii.ac.jp/crid/1360574095703842816","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Navier-Stokes Equations"}]},{"@id":"https://cir.nii.ac.jp/crid/1360586666958297984","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"$L_{p}$-estimates of the solution of a linear problem arising in magnetohydrodynamics"}]},{"@id":"https://cir.nii.ac.jp/crid/1360586667457611776","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"On the Stabilizing Effect of the Magnetic Fields in the Magnetic Rayleigh--Taylor Problem"}]},{"@id":"https://cir.nii.ac.jp/crid/1360586669493152000","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Global attractors for the three-dimensional Navier-Stokes equations"}]},{"@id":"https://cir.nii.ac.jp/crid/1360586669823695616","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Asymptotic Compactness of Global Trajectories Generated by the Navier–Stokes Equations of a Compressible Fluid"}]},{"@id":"https://cir.nii.ac.jp/crid/1360586670116196096","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Flux Separation in Stellar Magnetoconvection"}]},{"@id":"https://cir.nii.ac.jp/crid/1360586670978171904","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Ergodic theory for energetically open compressible fluid flows"}]},{"@id":"https://cir.nii.ac.jp/crid/1360868143117313280","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Mathematical Theory of Compressible Magnetohydrodynamics Driven by Non-conservative Boundary Conditions"}]},{"@id":"https://cir.nii.ac.jp/crid/1360868145861409664","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Solvability of an inhomogeneous boundary value problem for steady MHD equations"}]},{"@id":"https://cir.nii.ac.jp/crid/1360868145924674816","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Mathematics of Open Fluid Systems"}]},{"@id":"https://cir.nii.ac.jp/crid/1361137045187024512","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Navier-Stokes Equations and Turbulence"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262943585941376","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"An Introduction to the Mathematical Theory of the Navier-Stokes Equations"}]},{"@id":"https://cir.nii.ac.jp/crid/1362262943755286016","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"The Equations of Magnetohydrodynamics: On the Interaction Between Matter and Radiation in the Evolution of Gaseous Stars"}]},{"@id":"https://cir.nii.ac.jp/crid/1363107370691875072","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Inéquations en thermoélasticité et magnétohydrodynamique"}]},{"@id":"https://cir.nii.ac.jp/crid/1363388844772697984","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Some mathematical questions related to the mhd equations"}]},{"@id":"https://cir.nii.ac.jp/crid/1364233269699004544","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"Attractors representing turbulent flows"}]},{"@id":"https://cir.nii.ac.jp/crid/1364233270240754304","@type":"Article","relationType":["references"],"jpcoar:relatedTitle":[{"@value":"On the Equation div u = g and Bogovskii’s Operator in Sobolev Spaces of Negative Order"}]}],"dataSourceIdentifier":[{"@type":"JALC","@value":"oai:japanlinkcenter.org:2014481366"},{"@type":"NDL_SEARCH","@value":"oai:ndlsearch.ndl.go.jp:R000000004-I034225726"},{"@type":"CROSSREF","@value":"10.2969/jmsj/92789278"}]}