| Abstract: |
| We consider a system consisting of a surface Navier-Stokes equation for incompressible fluids on an elastic inextensible membrane, whose evolution is coupled to the flow of the fluid on the surface. This leads to a highly nonlinear quasilinear geometric evolution equation of parabolic-hyperbolic type. Using a suitable parametrization we linearize the system and obtain well-posedness of it in suitable $L^2$-type Sobolev spaces. With the aid of a suitable fixed-point argument we show existence of strong solutions locally in time. |
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