相关论文: A geometric trapping approach to global regularity…
In two and three space dimensions, and under suitable assumptions on the initial data, we show global existence for a damped wave equation which approaches, in some sense, the Navier-Stokes problem. The proofs are based on a refined energy…
We provide a proof of global regularity of solutions of coupled Navier-Stokes equations and Fokker-Planck equations, in two spatial dimensions, in the absence of boundaries. The proof yields a priori estimates for the growth of spatial…
Using ODE-methods and trapping regions derived by Mattingly and Sinai we give a new proof of the existence and uniqueness of solutions to Navier-Stokes equations with periodic boundary conditions on the plane.
We propose a microlocal-Riemannian framework for the three-dimensional incompressible Navier-Stokes equations on a smooth oriented Riemannian manifold (M,g). The dynamics is lifted to the unit cosphere bundle S*M via a normal-coordinate…
We study the global regularity, for all time and all initial data in $H^{1/2}$, of a recently introduced decimated version of the incompressible 3D Navier-Stokes (dNS) equations. The model is based on a projection of the dynamical evolution…
We give a geometric approach to proving know regularity and existence theorems for the 2D Navier-Stokes Equations. We feel this point of view is instructive in better understanding the dynamics. The technique is inspired by constructions in…
This paper gives another version of results due to Raugel and Sell, and similar results due to Moise, Temam and Ziane, that state the following: the solution of the Navier-Stokes equation on a thin 3 dimensional domain with periodic…
In this paper we give a proof of the existence of global regular solutions to the Fourier transformed Navier-Stokes system with small initial data in $\Phi(2)$ via an iteration argument. The proof of the regularity theorem is a minor…
In this paper, we consider the global regularity and the optimal time decay rate for the 2D isentropic hypo-viscous compressible Navier-Stokes equations. Firstly, we prove that there exists a global strong solution with the small initial…
The initial problem for the Navier-Stokes type equations over ${\mathbb R}^n \times [0,T]$, $n\geq 2$, with a positive time $T$ in the spatially periodic setting is considered. First, we prove that the problem induces an open injective…
The Navier-Stokes motions in a box with periodic boundary conditions are considered. First the existence of global regular two-dimensional solutions is proved. The solutions are such that continuous with respect to time norms are controlled…
Global regularity for the three-dimensional incompressible Navier-Stokes equations remains unresolved partly because weak, mild, and strong formulations employ incompatible functional settings. The present study introduces a…
In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian $3$-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This…
Direct methods to obtain global stability modes are restricted by the daunting sizes and complexity of Jacobians encountered in general three-dimensional flows. Jacobian-free iterative approaches such as Arnoldi methods have greatly…
In this lecture note, we study free boundary problems for the Navier-Stokes equations with and without surface tension. The local well-posedness, the global well-posedness, and asymptotics of solutions as time goes to infinity are studied…
In this paper, we will prove a new result that guarantees the global existence of solutions to the Navier--Stokes equation in three dimensions when the initial data is sufficiently close to being two dimensional. This result interpolates…
In 1999, J.C. Mattingly and Ya. G. Sinai used elementary methods to prove the existence and uniqueness of smooth solutions to the 2D Navier-Stokes equations with periodic boundary conditions. And they were almost successful in proving the…
The Navier--Stokes system is considered in a compact Riemannian manifold. Gevrey class regularity is proven under Lions boundary conditions: in 2D for the Rectangle, Cylinder, and Hemisphere, and in 3D for the Rectangle. The cases of the 2D…
In this article we study a system of equations that is known to {\em extend} Navier-Stokes dynamics in a well-posed manner to velocity fields that are not necessarily divergence-free. Our aim is to contribute to an understanding of the role…
We address the long-time behavior of the 2D Boussinesq system, which consists of the incompressible Navier-Stokes equations driven by a non-diffusive density. We construct globally persistent solutions on a smooth bounded domain, when the…