相关论文: An Elementary Proof of the Existence and Uniquenes…

This paper is a continuation of [26]. Here theorems on conditional uniqueness and regularity for solutions to stochastic Navier-Stokes equations in $\mathbb R^d$ are presented.

We consider the motion described by the Navier-Stokes equations in a box with periodic boundary conditions. First we prove the existence of global strong two-dimensional solutions. Next we show the existence of global strong…

We consider the initial value problem for the Navier-Stokes equations over $R^{3} \times [0,T]$ with a positive time $T$ in the spatially periodic setting. Identifying periodic vector-valued functions on $R^{3}$ with functions on the…

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…

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…

Existence, uniqueness, and regularity of time-periodic solutions to the Navier-Stokes equations in the three-dimensional whole-space are investigated. We consider the Navier-Stokes equations with a non-zero drift term corresponding to the…

The Navier-Stokes motions in cylindrical domain with Navier boundary conditions are considered. First the existence of global regular two-dimensional solutions are proved. The solutions are bounded by the same constant for all time.…

We prove, with a more geometric approach, that the solutions to the Navier-Stokes equations are regular up to a set of Hausdorff dimension 1. The main tool for the proof is a new compactness lemma and the monotonicity property of harmonic…

In this paper we first prove the existence and uniqueness of the solution to the stochastic Navier--Stokes equations on the rotating 2-dimensional sphere. Then we show the existence of an asymptotically compact random dynamical system…

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…

This paper discussed the existence and uniqueness of the smoothing solution of the Navier-Stokes equations. At first, we construct the theory of the linear equations which is about the unknown four variables functions with constant…

We study the two-dimensional stationary Navier-Stokes equations with rotating effect in the whole space. The unique existence and the asymptotics of solutions are obtained without the smallness assumption on the rotation parameter.

This paper proposes a computer-assisted solution existence verification method for the stationary Navier-Stokes equation over general 3D domains. The proposed method verifies that the exact solution as the fixed point of the Newton…

In this paper, we give a sufficient condition to guarantee the existence of a smooth solution of the Navier-Stokes Equation with the nice decreasing properties at infinity. In this way, we prove the existence of smooth physically reasonable…

We consider the initial problem for the Navier-Stokes equations over ${\mathbb R}^3 \times [0,T]$ with a positive time $T$ over specially constructed scale of function spaces of Bochner-Sobolev type. We prove that the problem induces an…

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…

We study the two-dimensional stationary Navier-Stokes equations describing the flows around a rotating obstacle. The unique existence of solutions and their asymptotic behavior at spatial infinity are established when the rotation speed of…

In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D Navier-Stokes equation in the whole space. In particular, if there exists a bounded smooth solution to the classical 3D Navier-Stokes equation, then…

The planar Navier-Stokes equation exhibits, in absence of external forces, a trivial asymptotics in time. Nevertheless the appearence of coherent structures suggests non-trivial intermediate asymptotics which should be explained in terms of…

We consider the Navier-Stokes equations on thin 3D domains, supplemented mainly with purely periodic boundary conditions or with periodic boundary conditions in the thin direction and homogeneous Dirichlet conditions on the lateral…