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タイトル	On Chorin’s method for stationary solutions of the incompressible Navier-Stokes equation
開催日時	2015年8月3日 16:45 ～
主催者
講演者	隠居 良行 氏（九大・数理）
場所	慶應義塾大学理工学部 14棟 733 (創想館 7階 ミーティング3)
内容	To find a stationary solution of the incompressible Navier-Stokes equation, A. Chorin proposed an artificial compressible system which is obtained by adding the time derivative of the pressure $\epsilon \partial_t p$ to the continuity equation for the incompressible fluid, where $\epsilon>0$ is a small parameter. If the solution of the artificial compressible system converges to a stationary solution, then the stationary solution is also a stationary solution of the incompressible Navier-Stokes equation. By using this method, Chorin numerically obtained stationary cellular convection solutions of the Oberbeck-Boussinesq equation in a domain between two parallel plates. In this talk I will consider a mathematical justification of Chorin's method. It will be shown that if a stationary solution of the incompressible Navier-Stokes equation is asymptotically stable, then it is also asymptotically stable as a stationary solution of the artificial compressible system for sufficiently small $\epsilon$. Problem is formulated as a kind of singular perturbation problem. The point of the proof is to control the spectrum of the "compressbile part" of the linearized operator. This talk is based on a joint work with Takaaki Nishida (Kyoto university).
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