We consider the Navier–Stokes system in a bounded domain with a smooth boundary. Given a sufficiently regular time-dependent global solution, we construct a finite-dimensional feedback control that is supported by a given open set and stabilizes the linearized equation. The proof of this fact is based on a truncated observability inequality, the regularizing property for the linearized equation...

Here ν = 0 for the Euler equation and ν > 0 for the Navier–Stokes equation. We assume that the initial vector field, v(x, 0) = u(x), is given by a smooth, bounded, divergence–free function u(x) of finite energy. Then a smooth solution v(x, t) is known to exist in some finite time interval 0 ≤ t < T . It is an open problem, for both the Euler and the Navier–Stokes equations, if blow–up can occur...

Approximated solutions to two-dimensional and axisymmetric jet impinging flows have been presented here. Assumptions have been made to reduce the related full Navier-Stokes equations to a non-linear ordinary differential equation. The Admomian decomposition method (ADM) has been employed to obtain an approximated solution to this differential equation. A trial and error strategy has been used t...

We construct the Navier-Stokes equation from first principle using relativistic bosonic lagrangian which is invariant under local gauge transformations. We show that by defining the bosonic field to represent the dynamic of fluid in a particular form, a general Navier-Stokes equation with conservative forces can be reproduced exactly. It also induces two new forces, one is relevant for rotation...

We establish the incompressible Navier–Stokes limit for the discrete velocity model of the Boltzmann equation in any dimension of the physical space, for densities which remain in a suitable small neighborhood of the global Maxwellian. Appropriately scaled families solutions of discrete Boltzmann equation are shown to have fluctuations that locally in time converge strongly to a limit governed ...

One shows that the Navier-Stokes equation in O⊂Rd, d = 2, 3, around an unstable equilibrium solution is exponentially stabilizable in probability by an internal noise controller V (t, ξ) = ∑N i=1 Vi(t)ψi(ξ)β̇i(t), ξ ∈ O, where {βi}i=1 are independent Brownian motions and {ψi}i=1 is a system of functions on O with support in an arbitrary open subset O0 ⊂ O. The stochastic control input {Vi}i=1 is...

We consider finite deformations of the p+ 2-dimensional Schwarzschild geometry which obey the vacuum Einstein equation, preserve the mean curvature and induced conformal metric on a sphere a distance λ from the horizon and are regular on the future horizon. We show perturbatively that in the limit λ → 0 the deformations are given by solutions of the nonlinear incompressible Navier-Stokes equati...

In this paper nonlocal boundary conditions for the Navier–Stokes equations are derived, starting from the Boltzmann equation in the hydrodynamic limit. Basing on phenomenological arguments, two scattering kernels which model non–local interactions between the gas molecules and the wall boundary are proposed. They satisfy the global mass conservation and a generalized reciprocity relation. The a...

Abstract. In this paper, we study the regularities of solutions of nonlinear stochastic partial differential equations in the framework of Hilbert scales. Then we apply our general result to several typical nonlinear SPDEs such as stochastic Burgers and Ginzburg-Landau’s equations on the real line, stochastic 2D Navier-Stokes equations in the whole space and a stochastic tamed 3D Navier-Stokes ...

In a recent paper [11], Vishik proved the global well-posedness of the two-dimensional Euler equation in the critical Besov space B 2,1. In the present paper we prove that Navier-Stokes system is globally well-posed in B 2,1, with uniform estimates on the viscosity. We prove also a global result of inviscid limit. The convergence rate in L is of order ν. keywords. navier-Stokes equations; Incom...