LIOUVILLE TYPE THEOREMS FOR THE STEADY AXIALLY SYMMETRIC NAVIER-STOKES AND MAGNETOHYDRODYNAMIC EQUATIONS
DC Field | Value | Language |
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dc.contributor.author | Chae, Dongho | - |
dc.contributor.author | Weng, Shangkun | - |
dc.date.available | 2019-01-22T14:23:06Z | - |
dc.date.issued | 2016-10 | - |
dc.identifier.issn | 1078-0947 | - |
dc.identifier.issn | 1553-5231 | - |
dc.identifier.uri | https://scholarworks.bwise.kr/cau/handle/2019.sw.cau/1727 | - |
dc.description.abstract | In this paper we study Liouville properties of smooth steady axially symmetric solutions of the Navier-Stokes equations. First, we provide another version of the Liouville theorem of [14] in the case of zero swirl, where we replaced the Dirichlet integrability condition by mild decay conditions. Then we prove some Liouville theorems under the assumption vertical bar vertical bar u(r)/r 1({ur < 1/r})vertical bar vertical bar(L3/2(R3)) < C-# where C-# is a universal constant to be specified. In particular, if u(r)(r,z) >= -1/r for for all(r, z) is an element of [0, infinity) x R, then u equivalent to 0. Liouville theorems also hold if lim(vertical bar x vertical bar ->infinity) Gamma = 0 or Gamma is an element of L-q(R-3) for some q is an element of [2, infinity) where Gamma = ru(theta). We also established some interesting inequalities for Omega :- delta(z)u(r)-delta(r)u(z)/r, showing that del Omega can be bounded by Omega itself. All these results are extended to the axially symmetric MHD and Hall-MHD equations with u = u(r)(r, z)e(r) + u(theta)(r, z)e(theta) + u(z)(r, z)e(z),h - h(theta)(r, z)e(theta), indicating that the swirl component of the magnetic field does not affect the triviality. Especially, we establish the maximum principle for the total head pressure Phi = 1/2(vertical bar u vertical bar(2) + vertical bar h vertical bar(2)) + p for this special solution class. | - |
dc.format.extent | 19 | - |
dc.publisher | AMER INST MATHEMATICAL SCIENCES-AIMS | - |
dc.title | LIOUVILLE TYPE THEOREMS FOR THE STEADY AXIALLY SYMMETRIC NAVIER-STOKES AND MAGNETOHYDRODYNAMIC EQUATIONS | - |
dc.type | Article | - |
dc.identifier.doi | 10.3934/dcds.2016031 | - |
dc.identifier.bibliographicCitation | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, v.36, no.10, pp 5267 - 5285 | - |
dc.description.isOpenAccess | N | - |
dc.identifier.wosid | 000385220600005 | - |
dc.identifier.scopusid | 2-s2.0-84979600062 | - |
dc.citation.endPage | 5285 | - |
dc.citation.number | 10 | - |
dc.citation.startPage | 5267 | - |
dc.citation.title | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | - |
dc.citation.volume | 36 | - |
dc.type.docType | Article | - |
dc.publisher.location | 미국 | - |
dc.subject.keywordAuthor | Steady Navier-Stokes equations | - |
dc.subject.keywordAuthor | Liouville type theorem | - |
dc.subject.keywordAuthor | axially symmetric solutions | - |
dc.subject.keywordPlus | HALL-MAGNETOHYDRODYNAMICS | - |
dc.subject.keywordPlus | REGULARITY | - |
dc.subject.keywordPlus | SYSTEM | - |
dc.relation.journalResearchArea | Mathematics | - |
dc.relation.journalWebOfScienceCategory | Mathematics, Applied | - |
dc.relation.journalWebOfScienceCategory | Mathematics | - |
dc.description.journalRegisteredClass | sci | - |
dc.description.journalRegisteredClass | scie | - |
dc.description.journalRegisteredClass | scopus | - |
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