Modeling Error of $\alpha$-Models of Turbulence on a Two-Dimensional Torus

They are entirely devoted to the initial value problem and the long-time behavior of solutions for the two-dimensional incompressible Navier–Stokes equations, in the particular

Thus, roughly speaking, Theorem 2 extends the uniqueness results of Prodi, Serrin, Sohr and von Wahl to some classes of weak solutions which.. are more regular in

The aim of this section is the proof of our main result, Theorem 4.1 below, that states the sequence of regular weak solutions converges to a solution of the mean

The proof is based on the weighted estimates of both pressure and kinetic energy for the approximate system which result in some higher integrability of the density, and the method

Keywords: Navier–Stokes equations; Uniqueness; Weak solution; Fourier localization; Losing derivative estimates.. In three dimensions, however, the question of regularity and

In this paper, we establish a small time large deviation principle (small time asymptotics) for the two-dimensional stochastic Navier–Stokes equations driven by multiplicative

In this paper, in order to approximate the solution of discretized problem (10, 11), we use the Galerkin method for the momentum and continuity equations which allows to circumvent

The main objective of the present work was to develop a finite-element algorithm for solving the two-dimensional incompressible Navier-Stokes equations with Canalis force, based