New approach to the incompressible Maxwell–Boussinesq approximation: Existence, uniqueness and shape sensitivity

0349631 - MÚ 2011 RIV US eng J - Journal Article
Consiglieri, L. - Nečasová, Šárka - Sokolowski, J.
New approach to the incompressible Maxwell–Boussinesq approximation: Existence, uniqueness and shape sensitivity.
Journal of Differential Equations. Roč. 249, č. 12 (2010), s. 3052-3080. ISSN 0022-0396. E-ISSN 1090-2732
R&D Projects: GA AV ČR IAA100190804; GA MŠMT LC06052
Institutional research plan: CEZ:AV0Z10190503
Keywords : magnetohydrodynamic flows * existence * uniqueness * shape sensitivity
Subject RIV: BA - General Mathematics
Impact factor: 1.261, year: 2010
http://www.sciencedirect.com/science/article/pii/S0022039610003669

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.
Permanent Link: http://hdl.handle.net/11104/0189817