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New approach to the incompressible Maxwell–Boussinesq approximation: Existence, uniqueness and shape sensitivity
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SYSNO ASEP 0349631 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title New approach to the incompressible Maxwell–Boussinesq approximation: Existence, uniqueness and shape sensitivity Author(s) Consiglieri, L. (PT)
Nečasová, Šárka (MU-W) RID, SAI, ORCID
Sokolowski, J. (FR)Source Title Journal of Differential Equations. - : Elsevier - ISSN 0022-0396
Roč. 249, č. 12 (2010), s. 3052-3080Number of pages 27 s. Language eng - English Country US - United States Keywords magnetohydrodynamic flows ; existence ; uniqueness ; shape sensitivity Subject RIV BA - General Mathematics R&D Projects IAA100190804 GA AV ČR - Academy of Sciences of the Czech Republic (AV ČR) LC06052 GA MŠMT - Ministry of Education, Youth and Sports (MEYS) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000284673000006 EID SCOPUS 78049244423 DOI 10.1016/j.jde.2010.09.029 Annotation The Boussinesq approximation to the Fourier–Navier–Stokes (F–N–S) flows under the electromagnetic field is considered. Such a model is the so-called Maxwell–Boussinesq approximation. We propose a new approach to the problem. We prove the existence and uniqueness of weak solutions to the variational formulation of the model. Some further regularity in W1,2+δ, δ>0, is obtained for the weak solutions. The shape sensitivity analysis by the boundary variations technique is performed for the weak solutions. As a result, the existence of the strong material derivatives for the weak solutions of the problem is shown. The result can be used to establish the shape differentiability for a broad class of shape functionals for the models of Fourier–Navier–Stokes flows under the electromagnetic field. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2011
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