相关论文: Strong solutions to the Navier-Stokes equations on…

We consider the Navier-Stokes equations in a three-dimensional curved thin domain around a given closed surface under Navier's slip boundary conditions. When the thickness of the thin domain is sufficiently small, we establish the global…

The weak solution to the Navier-Stokes equations in a bounded domain $D \subset \mathbb{R}^3$ with a smooth boundary is proved to be unique provided that it satisfies an additional requirement. This solution exists for all $t \geq 0$. In a…

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…

The nonhomogeneous Navier-Stokes equations with density-dependent viscosity is studied in three-dimensional (3D) exterior domains with nonslip or slip boundary conditions. We prove that the strong solutions exists globally in time provided…

We examine the so-called micropolar equations in three dimensional cylindrical domains under Navier boundary conditions. These equations form a generalization of the ordinary incompressible Navier-Stokes model, taking the structure of the…

We consider the Navier-Stokes system describing the time evolution of a compressible barotropic fluid confined to a bounded spatial domain in the 3-D physical space, supplemented with the Navier's slip boundary conditions. It is shown that…

In this note we give a criterion for the existence of global strong solutions for the 3D Navier-Stokes system for any regular initial data.

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…

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.…

Regularity properties of strong solutions are considered.

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…

The micropolar equations are a useful generalization of the classical Navier-Stokes model for fluids with micro-structure. We prove the existence of global and strong solutions to these equations in cylindrical domains in $\mathbb{R}^3$. We…

Stochastic Navier--Stokes equations in a thin three-dimensional domain are considered, driven by additive noise. The convergence of martingale solution of the stochastic Navier--Stokes equations in a thin three-dimensional domain to the…

Onsager's conjecture for the 3D Navier-Stokes equations concerns the validity of energy equality of weak solutions with regards to their smoothness. In this note we establish energy equality for weak solutions in a large class of function…

We prove the existence of a weak solution to the three-dimensional steady compressible isentropic Navier-Stokes equations in bounded domains for any specific heat ratio \gamma > 1. Generally speaking, the proof is based on the new weighted…

We consider the Navier-Stokes equations with Navier's slip boundary conditions in a three-dimensional curved thin domain around a given closed surface. Under suitable assumptions we show that the average in the thin direction of a strong…

A proof of existence, uniqueness and smoothness of the Navier-Stokes equations is an actual problem, which solution is important for different branches of science. The subject of this study is obtaining the smooth and unique solutions of…

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…

In this paper, we consider the smooth solutions of 3D incompressible Navier-Stokes equations in periodic domains. We prove that, in the absence of external forces and with divergence-free smooth periodic initial data, periodic smooth…

In this paper, we consider the three-dimensional inhomogeneous Navier-Stokes equations with density-dependent viscosity in presence of vacuum over bounded domains. Global-in-time unique strong solution is proved to exist when $\|\nabla…