Abstract
We investigate the stability and global existence of weak solutions to a free boundary problem governing the evolution of polymeric fluids. We construct weak solutions of the two-phase model by performing the asymptotic limit of a macroscopic model governing the suspensions of rod-like molecules (known as Doi-model) in compressible fluids as the adiabatic exponent \(\gamma \) goes to \(\infty .\) The convergence of these solutions, up to a subsequence, to the free-boundary problem is established using techniques in the spirit of Lions and Masmoudi (Ann Inst Henri Poincaré 16:373–410, 1999).
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Donatelli, D., Trivisa, K. On a free boundary problem for polymeric fluids: global existence of weak solutions . Nonlinear Differ. Equ. Appl. 24, 51 (2017). https://doi.org/10.1007/s00030-017-0475-5
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DOI: https://doi.org/10.1007/s00030-017-0475-5
Keywords
- Doi model
- Suspensions of rod-like molecules
- Fluid-particle interaction model
- Compressible Navier–Stokes equations
- Fokker–Planck-type equation
- Free boundary problems