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Incompressible Maxwell-Boussinesq approximation: Existence, uniqueness and shape sensitivity

Consiglieri L., Necasova S., Sokolowski J.

Control and Cybernetics

2009

Vol. 38, no 4A

1193-1215

We prove the existence and uniqueness of weak solutions to the variational formulation of the Maxwell-Boussinesq approximation problem. 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.