Field correlators in QCD. Theory and applications. Abstract This review is dedicated to the study of nonabelian gauge theories by making use of the gauge-invariant nonlocal field correlators. Basic theoretical aspects, such as nonabelian Stokes theorem, cluster expansion , Gaussian dominance as well as numerous phenomenological applications are reviewed.

This paper reviews the recent progress on stochastic PDEs arising from different aspects of the turbulence theory including the stochastic Navier-Stokes equation, stochastic Burgers equation and stochastic passive scalar and passive vector equations. Issues discussed include the existence of invariant measures, scaling of the structure functions, asymptotic behavior of the probability density f...

We develop the theory of degenerate and nonlinear evolution systems in mixed formulation. It will be shown that many of the well-known results for the stationary problem extend to the nonlinear case and that the dynamics of a degenerate Cauchy problem is governed by a nonlinear semigroup. The results are illustrated by a Darcy–Stokes coupled system with multiple nonlinearities.

The influence of boundary roughness characteristics on the rate of dissipation in a viscous fluid is analyzed using shape calculus from the theory of optimal control of systems governed by partial differential equations. To study the mapping D from surface roughness topography to the dissipation rate of a Navier–Stokes flow, expressions for the shape gradient and Hessian are determined using th...

Some important concepts in the nonstandard analysis theory of turbulence are presented in this article. The structure of point, on which differential equations are defined, is analyzed. The distinction between the uniform point and the non-uniform point, as well as between the standard point and the nonstandard point, is showed. A new kind of equations, which differ essentially from those in ex...

The extension of the Geometrical Theory of Diiraction to complex rays is considered. The key diierence with real rays arises in the determination of the regions of existence of the incident and reeected elds, which are governed by Stokes phenomenon. The procedure is demonstrated using the simple example of diiraction by a nite plate.

The projection multilevel method can be an efficient solver for systems of nonlinear partial differential equations that, for certain classes of nonlinearities (including least-squares formulations of the Navier-Stokes equations), requires no linearization anywhere in the algorithm. This paper provides an abstract framework and establishes optimal V-cycle convergence theory for this method.

We develop a dynamical systems theory for the compressible Navier-Stokes equations based on global in time weak solutions. The following questions will be addressed: • Global existence and critical values of the adiabatic constant; • dissipativity in the sense of Levinson bounded absorbing sets; • asymptotic compactness; • the long-time behaviour and attractors. 2000 Mathematics Subject Classif...

We present a technique that allows to obtain certain results in the compressible fluid theory: in particular, it is a nonexistence result for the highly decreasing at infinity solutions to the Navier-Stokes equations, the construction of the solutions with uniform deformation and the study of behavior of the boundary of a material volume of liquid.