Newtonian limit of Maxwell fluid flows

In this paper, we revise Maxwell's constitutive relation and formulate a system of first-order partial differential equations with two parameters for compressible viscoelastic fluid flows. The system is shown to possess a nice conservation-dissipation (relaxation) structure and therefore is symmetrizable hyperbolic. Moreover, for smooth flows we rigorously verify that the revised Maxwell's constitutive relations are compatible with Newton's law of viscosity.Comment: 11 page

Conservation-Dissipation Formalism for Soft Matter Physics: I. Equivalence with Doi's Variational Approach

In this paper, we proved that by choosing the proper variational function and variables, the variational approach proposed by M. Doi in soft matter physics was equivalent to the Conservation-Dissipation Formalism. To illustrate the correspondence between these two theories, several novel examples in soft matter physics, including particle diffusion in dilute solutions, polymer phase separation dynamics and nematic liquid crystal flows, were carefully examined. Based on our work, a deep connection among the generalized Gibbs relation, the second law of thermodynamics and the variational principle in non-equilibrium thermodynamics was revealed.Comment: 21 page

The optimal decay estimates for the Euler-Poisson two-fluid system

This work is devoted to the optimal decay problem for the Euler-Poisson two-fluid system, which is a classical hydrodynamic model arising in semiconductor sciences. By exploring the influence of the electronic field on the dissipative structure, it is first revealed that the \textit{irrotationality} plays a key role such that the two-fluid system has the same dissipative structure as generally hyperbolic systems satisfying the Shizuta-Kawashima condition. The fact inspires us to give a new decay framework which pays less attention on the traditional spectral analysis. Furthermore, various decay estimates of solution and its derivatives of fractional order on the framework of Besov spaces are obtained by time-weighted energy approaches in terms of low-frequency and high-frequency decompositions. As direct consequences, the optimal decay rates of $L^{p}(\mathbb{R}^{3})$-$L^{2}(\mathbb{R}^{3})(1\leq p<2)$ type for the Euler-Poisson two-fluid system are also shown.Comment: 40pages. arXiv admin note: text overlap with arXiv:1402.468