Abstract. Moments of the vorticity are used to define and estimate a hierarchy of time-averaged inverse length scales for weak solutions of the three-dimensional, incompressible Navier-Stokes equations on a periodic box. The estimate for the smallest of these inverse scales coincides with the inverse Kolmogorov length, but thereafter the exponents of the Reynolds number rise rapidly for corresp...

The existence of infinitely many weak solutions for a Navier doubly eigenvalue boundary value problem involving the $p(x)$-biharmonic operator is established. In our main result, under an appropriate oscillating behavior of the nonlinearity and suitable assumptions on the variable exponent, a sequence of pairwise distinct solutions is obtained. Furthermore, some applications are pointed out.

The properties of solutions for a parabolic system with homogeneous Dirichlet boundary conditions, which arises in a cooperating three-species food chain model, are investigated. ‘It is shown that global solutions exist if the intraspecific competitions are strong whereas blowup solutions exist under certain conditions if the intra-specific competitions are weak. @ 2004 Elsevier Ltd. All rights...

Enstrophy, half the integral of the square of vorticity, plays a role in 2D turbulence theory analogous to that played by kinetic energy in the Kolmogorov theory of 3D turbulence. It is therefore interesting to obtain a description of the way enstrophy is dissipated at high Reynolds number. In this article we explore the notions of viscous and transport enstrophy defect, which model the spatial...

the aim of this article is to establish the existence of at least three‎ ‎solutions for a perturbed $p$-biharmonic equation depending on two‎ ‎real parameters‎. ‎the approach is based on variational methods‎.

This paper we investigate the existence and uniqueness of solutions to fuzzydierential equations driven by Liu's process. For this, it is necessary to provideand prove a new existence and uniqueness theorem for fuzzy dierential equationsunder weak Lipschitz condition. Then the results allows us to considerand analyze solutions to a wide range of nonlinear fuzzy dierential equationsdriven by Liu...

We consider the behaviour of weak solutions of the unforced threedimensional Navier-Stokes equations, under the assumption that the initial condition has finite energy (‖u‖2 = ∫ |u|2) but infinite enstrophy (‖Du‖2 = ∫ |curlu|2). We show that this has to be reflected in the solution for small times, so that in particular ‖Du(t)‖ → +∞ as t → 0. We also give some limitations on this ‘backwards blo...

In this paper, three dimensional (3D) static and dynamic analysis of thick plates based on the Meshless Local Petrov-Galerkin (MLPG) is presented. Using the kinematics of a three-dimensional continuum, the local weak form of the equilibrium equations is derived. A weak formulation for the set of governing equations is transformed into local integral equations on local sub-domains by using a uni...