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 $$\gamma $$ γ 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).
Nonlinear Differential Equations and Applications NoDEA – Springer Journals
Published: Aug 5, 2017
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