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In this paper, we revise Maxwells 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 Maxwells constitutive relations are compatible with Newtons law of viscosity.
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the density of
We prove rigorously that the exact N-electron Hohenberg-Kohn density functional converges in the strongly interacting limit to the strictly correlated electrons (SCE) functional, and that the absolute value squared of the associated constrained-searc
We develop a model of an electrorheological fluid such that the fluid is considered as an anisotropic one with the viscosity depending on the second invariant of the rate of strain tensor, on the module of the vector of electric field strength, and o
We consider the Fermi-Pasta-Ulam-Tsingou (FPUT) chain composed by $N gg 1$ particles and periodic boundary conditions, and endow the phase space with the Gibbs measure at small temperature $beta^{-1}$. Given a fixed ${1leq m ll N}$, we prove that the
In the study of ocean wave impact on structures, one often uses Froude scaling since the dominant force is gravity. However the presence of trapped or entrained air in the water can significantly modify wave impacts. When air is entrained in water in