Some Fluid-Structure Interacting and Incompressible Limit Problems in Mathematical Fluid Mechanics(1/2)

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.