This paper proposes four fundamental requirements for establishing PDEs (partial
differential equations) modelling irreversible processes. We show that the PDEs derived via …

The generalized bracket framework is used to derive a family of compressible viscoelastic
models. The framework accounts for both reversible and non-reversible dynamics and …

Travelling wave solutions of the front, kink or shock wave type are obtained analytically for
one–dimensional viscoelastic Burgers equations with an objective Gordon–Schowalter time …

In this paper, we prove the global existence of general small solutions to compressible
viscoelastic system. We remove the “initial state” assumption (ρ _0\det F_0= 1 ρ~ 0 det F 0 …

The goal of this paper is to derive governing equations for complex fluids in a
thermodynamically consistent way so that the conservation of energy and the increase of …

We are interested in the multi-dimensional compressible viscoelastic flows of Oldroyd type,
which is one of non-Newtonian fluids exhibiting the elastic behavior. In order to capture the …

The main purpose of this review is to summarize the recent advances of the Conservation–
Dissipation Formalism (CDF), a new way for constructing both thermodynamically …

In the first paper of this series, we prove that by choosing the proper variational function and
variables, the variational approach proposed by Doi in soft matter physics is equivalent to …

In this paper we consider general port-Hamiltonian formulations of multidimensional
Maxwell's viscoelastic fluids. Two different cases are considered to describe the energy …

The global existence of solutions to incompressible viscoelastic flows has been a
longstanding open problem, even for the global weak solution. Under some special structure …