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Strong solution for polymeric fluid-structure interaction with small initial acceleration
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Strong solution for polymeric fluid-structure interaction with small initial acceleration
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We consider the problem of a 3D-3D-2D mutually coupled solute-solvent-structure three-states system. This describes the interaction of a flexible structure with a polymeric fluid of classical Oldroyd-B type without centre-of-mass diffusion. We construct a unique higher-order regularity notion of a strong solution for the system by decoupling the solute from the solvent-structure subsystem, solving the decoupled system individually, and gluing the solutions through a fixed-point argument. As a requirement for the construction, we rely on a maximal regularity result for the Stokes problem on moving domains with non-trivial boundary conditions; a result that is also of independent interest.
Forward citations
Cited by 2 Pith papers
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Well-posedness theorems in fluid-structure interaction: perfectly elastic shells
Local well-posedness is shown for 3D fluid-2D elastic shell interaction, with global extension in the 2D fluid-1D shell case until possible self-intersection.
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The simplified 2D Ericksen-Leslie liquid crystal model interacting with a 1D flexible shell
Global weak solutions exist for the simplified 2D Ericksen-Leslie liquid crystal model coupled to a 1D flexible shell, with convergence of Ginzburg-Landau approximations to the unapproximated system barring shell dege...
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