在這個計畫中我們提出三個數學問題：一、不可延展的囊泡與黏滯流體的交互作用：在這個子計畫中我們探討一個已經在數值模擬界被廣泛研究的流構耦合問題，試著提供這個模型的解存在之數學理論。二、具科氏力的流體之不可壓縮極限：在這個子計畫中我們探討一具科氏力作用的可壓縮流體在馬赫數與羅斯比數在特定方式趨近到零的情況之下，可壓縮流之解的強收斂行為。三、給定雅可比行列式與邊界值之微晶同構：在這個子計畫中我們探討如何在給定一微晶同構的雅可比行列式與邊界條件之下建構出該微晶同構。我們將聚焦在取得解在解空間中的估計。 ;In this project we propose three problems:1. Inextensible vesicle interacting with viscous: In this sub-project we study a fluid-structure interaction problem that is well-studied in the society of numerical simulations. We try to provide the existence theory of solutions to the model people used to perform numerical simulations.2. The incompressible limit of flows with Coriolis force: In this sub-project we study the incompressible limit problem of compressible fluids with Coriolis force when Rossby number and Mach number approaches zero in a specific way. We focus on the strong convergence instead of the weak convergence of the solution to the compressible fluids.3. Diffeomorphism with prescribing Jacobian and boundary data: In this sub-project we focus on the construction of a diffeomorphism whose Jacobian and boundary data are prescribed. We focus on providing estimates of solutions with given data.
