Speaker
Description
Viscoelastic phase separation plays an important role in biological cells, for instance, RNA or proteins can undergo phase separation to form membrane-less condensates, which is crucial for biological functions. In our contribution, we consider a model for phase separation in polymer solutions consistent with the second law of thermodynamics, introduced by Zhou et al. 2006. For the full model with additional stress diffusion, existence of global-in-time weak solutions is established by Brunk–Lukáčová-Medvid’ová 2022 via a Faedo–Galerkin ansatz for both degenerate and non-degenerate mobilities.
In this talk, we neglect the hydrodynamic transport and consider a constant mobility and a regular potential. Moreover, we focus on the case of a constant bulk modulus and a constant relaxation time. Exploiting the gradient-flow structure, we establish the global well-posedness (meaning existence, uniqueness and stability estimate) of the initial-boundary-value problem using a time-incremental minimisation scheme. We then address a singular limit through evolutionary $\Gamma$-convergence and Evolutionary Variational Inequality (EVI) solutions, tackling the primary challenge posed by the lack of equi-compactness of the energies.
This is a joint work with Katharina Hopf (WIAS) and Matthias Liero (WIAS).
