2024/01/18 by Henrot, Antoine, Mazari-Fouquer, Idriss, Privat, Yannick · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics #Optimization and Control (math.OC)
paper · doi:10.48550/arxiv.2401.09801
The goal of this paper is to investigate the minimisation of the first eigenvalue of the (vectorial) incompressible Dirichlet-Stokes operator. After providing an existence result, we investigate optimality conditions and we prove the following surprising result: while the ball satisfies first and second-order optimality conditions in dimension 2, it does not in dimension 3, so that the Faber-Krahn inequality for the Stokes operator is probably true in ℝ2, but does not hold in ℝ3. The multiplicity of the first eigenvalue of the Dirichlet-Stokes operator in the ball in ℝ3 plays a crucial role in the proof of that claim.