Global generalized solutions for Maxwell-alpha and Euler-alpha equations [PDF]
, 2010 We study initial-boundary value problems for the Lagrangian averaged alpha models for the equations of motion for the corotational Maxwell and inviscid fluids in 2D and 3D. We show existence of (global in time) dissipative solutions to these problems. We also discuss the idea of dissipative solution in an abstract Hilbert space framework.
arxiv +1 more source
Energy-variational solutions for viscoelastic fluid models
Advances in Nonlinear AnalysisIn this article, we introduce the concept of energy-variational solutions for a class of nonlinear dissipative evolutionary equations, which turns out to be especially suited to treat viscoelastic fluid models.
Agosti Abramo +2 more
doaj +1 more source
On infinite order differential operators in fractional viscoelasticity [PDF]
Fract. Calc. Appl. Anal., Vol 20, No 4 (2017), pp. 854-867, 2017 In this paper we discuss some general properties of viscoelastic models defined in terms of constitutive equations involving infinitely many derivatives (of integer and fractional order). In particular, we consider as a working example the recently developed Bessel models of linear viscoelasticiy that, for short times, behave like fractional Maxwell ...
arxiv +1 more source
Incompressible limit for the compressible viscoelastic fluids in critical space
Advances in Nonlinear AnalysisIn this article, we consider the incompressible limit of global-in-time strong solutions with arbitrary large initial velocity for the compressible viscoelastic fluids in the sense of critical Besov framework. We decouple our compressible system into two
Han Bin, Wu Dan
doaj +1 more source
On transient waves in linear viscoelasticity [PDF]
Wave Motion 74C (2017) pp. 191-212, 2017 The aim of this paper is to present a comprehensive review of method of the wave-front expansion, also known in the literature as the Buchen-Mainardi algorithm. In particular, many applications of this technique to the fundamental models of both ordinary and fractional linear viscoelasticity are thoroughly presented and discussed.
arxiv +1 more source
George William Scott Blair -- the pioneer of factional calculus in rheology [PDF]
, 2014 The article shows the pioneering role of the British scientist, Professor G.W.Scott Blair, in the creation of the application of fractional modelling in rheology. Discussion of his results is presented. His approach is highly recognized by the rheological society and is adopted and generalized by his successors.
arxiv +1 more source
Non-linear Langevin model for the early-stage dynamics of electrospinning jets [PDF]
, 2015 We present a non-linear Langevin model to investigate the early-stage dynamics of electrified polymer jets in electrospinning experiments. In particular, we study the effects of air drag force on the uniaxial elongation of the charged jet, right after ejection from the nozzle.
arxiv +1 more source
New entropy estimates for the Oldroyd-B model, and related models [PDF]
arXiv, 2007 This short note presents the derivation of a new {\it a priori} estimate for the Oldroyd-B model. Such an estimate may provide useful information when investigating the long-time behaviour of macro-macro models, and the stability of numerical schemes.
arxiv
Euler equation for incompressible non-Newtonian fluids: finite speed of propagations and asymptotic behavior of weak solutions [PDF]
arXiv, 2007 We investigate multidimensional model for incompressible non-Newtonian fluids. Using method of energy estimates we prove the property of finite speed of propagations of the solution support for this problem. We find sharp bounds of the propagations by $L^2$--norm and $L^1$--norm of initial data.
arxiv
Global Strong Solution to the Density-Dependent Incompressible Viscoelastic Fluids [PDF]
arXiv, 2009 The existence and uniqueness of the global strong solution with small initial data to the three-dimensional viscoelastic fluids is established.
arxiv