In the present contribution, we first prove the existence of $\mathbf {m} $-fold simply-
connected V-states close to the unit disc for Euler-$\alpha $ equations. These solutions are …

We consider the vanishing viscosity limit of the Navier--Stokes equations in a half-plane,
with Dirichlet boundary conditions. We prove that the inviscid limit holds in the energy norm …

The dependence of the fractal dimension of global attractors for the damped 3D Euler–
Bardina equations on the regularization parameter α> 0 and Ekman damping coefficient γ> …

The second-grade fluid equations are a model for viscoelastic fluids, with two parameters:
α> 0, corresponding to the elastic response, and ν> 0 ν> 0, corresponding to viscosity …

Strong convergence of the vorticity and conservation of the energy for the α-Euler equations
Page 1 Nonlinearity PAPER • OPEN ACCESS Strong convergence of the vorticity and …

The Euler-α equations model the averaged motion of an ideal incompressible fluid when
filtering over spatial scales smaller than α. We show that there exists β> 1 such that weak …

We discuss the estimates for the $ L^ p $-norms of systems of functions that are orthonormal
in $ L^ 2$ and $ H^ 1$, respectively, and their essential role in deriving good or even …

We consider in a smooth bounded and simply connected two dimensional domain the
convergence in the L 2 norm, uniformly in time, of the solution of the stochastic second …

The theory of turbulent Newtonian fluids shows that the choice of the boundary condition is a
relevant issue because it can modify the behavior of a fluid by creating or avoiding a strong …

Using a weak convergence approach, we establish a Large Deviation Principle (LDP) for the
solutions of fluid dynamic systems in two-dimensional bounded domains subjected to no …