Domain perturbation problem for the Stokes equations and its application

2017 Fiscal Year Final Research Report

• Project/Area Number: 26800073
• Research Category: Grant-in-Aid for Young Scientists (B)
• Allocation Type: Multi-year Fund
• Research Field: Mathematical analysis
• Research Institution: Yokohama National University (2016-2017); Tamagawa University (2014-2015)
• Principal Investigator: Ushikoshi Erika 横浜国立大学, 大学院環境情報研究院, 講師 (20714041)
• Project Period (FY): 2014-04-01 – 2018-03-31
• Keywords: ストークス方程式 / アダマール変分公式

Outline of Final Research Achievements

In this research, our aim is to analyze the domain dependency of the Green function and the eigenvalues of the Stokes equations with the Dirichlet boundary condition.
As a result, we succeeded to establish the Hadamard variational formula for the Green function for the velocity and pressure under the general second order domain perturbations. Moreover, we composed the variational formula for the multiple eigenvalues, and we succeeded to apply that formula to clarify the topological type of the domain.

Free Research Field

偏微分方程式