2014/01/01 by Harald Garcke, Garcke, Harald, Claudia Hecht +1 · 3 citations
Computer Science · Engineering · Materials Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Advanced Numerical Methods in Computational Mathematics #Block Copolymer Self-Assembly #FOS: Mathematics #Optimization and Control (math.OC) #Solidification and crystal growth phenomena #math.OC
paper · pdf · doi:10.48550/arxiv.1407.5470
arxiv created 2014/07/21 · openalex publication_date 2014/07/21 · arxiv updated 2014/07/22 · openalex created_date 2022/10/02 · openalex updated_date 2026/07/28
We apply a phase field approach for a general shape optimization problem of a stationary Navier-Stokes flow. To be precise we add a multiple of the Ginzburg--Landau energy as a regularization to the objective functional and relax the non-permeability of the medium outside the fluid region. The resulting diffuse interface problem can be shown to be well-posed and optimality conditions are derived. We state suitable assumptions on the problem in order to derive a sharp interface limit for the minimizers and the optimality conditions. Additionally, we can derive a necessary optimality system for the sharp interface problem by geometric variations without stating additional regularity assumptions on the minimizing set.