相关论文: Almost Periodic Solutions and Global Attractors of…
We introduce and analyze a space-time least-squares method associated to the unsteady Navier-Stokes system. Weak solution in the two dimensional case and regular solution in the three dimensional case are considered. From any initial guess,…
In this paper, we investigate the existence of a unique global smooth solution to the three-dimensional incompressible Navier-Stokes equations and provide a concise proof. We establish a new global well-posedness result that allows the…
A sufficient condition of regularity for solutions to the Navier-Stokes equations is proved. It generalizes the so-called $L_{3,\infty}$-case.
We study the compressible quantum Navier-Stokes (QNS) equations with degenerate viscosity in the three dimensional periodic domains. On the one hand, we consider QNS with additional damping terms. Motivated by the recent works [Li-Xin,…
As in our previous paper, the 3D Navier-Stokes equations with a translationally bounded force contain pullback attractors in a weak sense. Moreover, those attractors consist of complete bounded trajectories. In this paper, we present a…
In this work we introduce and analyse a new low-order method for the variable-density incompressible Navier-Stokes equations. The main novelty of the proposed method lies in the support of general meshes, possibly including polygonal or…
The global existence of martingale solutions to the compressible Navier-Stokes equations driven by stochastic external forces, with density-dependent viscosity and vacuum, is established in this paper. This work can be regarded as a…
We propose a global scheme for a controlled Navier-Stokes equation system on compact smooth Riemannian manifolds.
This paper concerns the existence of global weak solutions to the barotropic compressible Navier-Stokes equations with degenerate viscosity coefficients. We construct suitable approximate system which has smooth solutions satisfying the…
The analysis of the long-term behavior of the mathematical model of a neural network constitutes a suitable framework to develop new tools for the dynamical description of nonautonomous state-dependent delay equations (SDDEs). The concept…
In this paper, we study the long-time dynamics of 3D non-autonomous Navier-Stokes-Voigt(NSV) equations with delay. Inspired by [36], we use the contractive function method to prove the pullback D-asymptotical compactness and existence of…
A few basic, intuitive, properties of the Navier-Stokes system of equations for incompressible fluid flows are discussed in this paper. We present a rephrased interpretation of the Navier-Stokes equation in a space having an arbitrary…
In this paper, we investigate a calmed version of the 3$D$ rotational Navier-Stokes equations driven by additive noise. First, we use the Ornstein-Uhlenbeck process to transform the equation into a random one. By using the Galerkin…
We establish the global existence and uniqueness of classical solutions to the three-dimensional full compressible Navier-Stokes system with smooth initial data which are of small energy but possibly large oscillations where the initial…
We establish the existence and uniqueness of the maximal pathwise solution for an abstract nonlinear stochastic evolutional equation, which takes the two and three dimensional stochastic Navier-Stokes equations as a typical model, forced by…
The paper is aimed at analysing a singular perturbation of the Navier-Stokes equations on a compact closed manifold. The case of compact smooth manifolds with boundary under the Dirichlet conditions is also included. Global existence and…
This article establishes estimates on the dimension of the global attractor of the two-dimensional rotating Navier-Stokes equation for viscous, incompressible fluids on the $\beta$-plane. Previous results in this setting by M.A.H.…
We prove the global existence of weak solutions to the isentropic compressible Navier-Stokes equations with ripped density in the half-plane under a slip boundary condition provided the bulk viscosity coefficient is properly large.…
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…
The global regularity problem for the periodic Navier-Stokes system asks whether to every smooth divergence-free initial datum $u_0: (\R/\Z)^3 \to \R^3$ there exists a global smooth solution u. In this note we observe (using a simple…