The fundamental importance of functional differential equations has been recognized in
many areas of mathematical physics, such as fluid dynamics (Hopf characteristic functional …

Nonlinear Systems and Their Remarkable Mathematical Structures, Volume 1 aims to
describe the recent progress in nonlinear differential equations and nonlinear dynamical …

It was shown by Oberlack and Rosteck [Discr. Cont. Dyn. Sys. S, 3, 451 2010 1937-1632
10.3934/dcdss. 2010.3. 451] that the infinite set of multipoint correlation (MPC) equations of …

The present article is intended to give a broad overview and present details on the Lie
symmetry induced statistical turbulence theory put forward by the authors and various other …

We consider a formulation for the Hopf functional differential equation which governs
statistical solutions of the Navier-Stokes equations. By introducing an exponential operator …

A detailed theoretical investigation is given which demonstrates that a recently proposed
statistical scaling symmetry is physically void. Although this scaling is mathematically …

In the present work, scaling laws for special turbulent flow phenomena are investigated
using a mathematical method based on Lie-point symmetries. Moreover, the theoretical …

In this paper, we extend the classical Lie symmetry analysis from partial differential
equations to integro-differential equations with functional derivatives. We continue the work …

,” Arch. Mech. 58, 597 (2006)] where Lie group theory has been extended to functional
differential equations and a special solution of the functional formulation of the Burgers …

The problem of finding Lie point symmetries for a certain class of multi-dimensional
nonlinear partial fractional differential equations and their systems is studied. It is assumed …