ASYMPTOTIC BEHAVIOR OF STRONG SOLUTIONS TO 2D g-NAVIER-STOKES EQUATIONS

Asymptotic Behavior of Solutions to the Full Compressible Navier-stokes Equations in the Half Space

Abstract. The one-dimensional motion of compressible viscous and heat-conductive fluid is investigated in the half space. By examining the sign of fluid velocity prescribed on the boundary, initial boundary value problems with Dirichlet type boundary conditions are classified into three cases: impermeable wall problem, inflow problem and outflow problem. In this paper, the asymptotic stability ...

Asymptotic Behavior of the Energy and Pointwise Estimates for Solutions to the Navier–stokes Equations

We study the large time behavior of the energy of a class of Navier–Stokes flows in Rn (n ≥ 2) with special symmetries. Inside this class, weconstruct examples of solutions such that the energy norm decays faster thant−(n+2)/4. Institut Girard Desargues, Université Lyon 1, 21, avenue Clude Bernard, 69622Villeurbanne Cedex, FRANCE, e-mail: [email protected]

Asymptotic Structure for Solutions of the Navier–stokes Equations

We study in this article the large time asymptotic structural stability and structural evolution in the physical space for the solutions of the 2-D NavierStokes equations with the periodic boundary conditions. Both the Hamiltonian and block structural stabilities and structural evolutions are considered, and connections to the Lyapunov stability are also given.

Strong Solutions of the Navier-Stokes Equations in Aperture Domains

Moments for strong solutions of the 2D stochastic Navier-Stokes equations in a bounded domain

We address a question posed by Glatt-Holtz and Ziane in [GHZ09, Remark 2.1 (ii)], regarding moments of strong pathwise solutions to the Navier-Stokes equations in a two-dimensional bounded domain O. We prove that Eφ(‖u(t)‖2H1(O)) < ∞ for any deterministic t > 0, where φ(x) = log(1 + log(1 + x)). Such moment bounds may be used to study statistical properties of the long time behavior of the equa...