相关论文: Remarks on the regularity criteria of generalized …

We show that any weak solution to the full Navier-Stokes-Fourier system emanating from the data belonging to the Sobolev space W^{3,2} remains regular as long as the velocity gradient is bounded. The proof is based on the weak-strong…

We derive a class of Navier--Stokes--Cahn--Hilliard systems that models two-phase flows with mass transfer coupled to the process of chemotaxis. These thermodynamically consistent models can be seen as the natural Navier--Stokes analogues…

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…

Mixed boundary value problems for the Navier-Stokes system in a polyhedral domain are considered. Different boundary conditions (in particular, Dirichlet, Neumann, slip conditions) are prescribed on the faces of a polyhedron. The authors…

In this paper, we investigate Liouville type theorems for the three-dimensional steady-state MHD or Hall-MHD system under some asymptotic assumptions at infinity. Firstly, for the Hall-MHD system we obtain that $u$ and $B$ are constant…

We prove existence of global regular axially-symmetric solutions to the Navier-Stokes equations in a cylindrical domain. We assume the periodic boundary conditions on the top and the bottom of the cylinder, but on the lateral part we assume…

We construct a large family of evidently integrable Hamiltonian systems which are generalizations of the KM system. The Hamiltonian vector field is homogeneous cubic but in a number of cases a simple change of variables transforms such a…

In this short survey paper, we focus on some new developments in the study of the regularity or potential singularity formation for solutions of the 3D Navier-Stokes equations. Some of the motivating questions are: Are certain norms…

Two unusual time-integral conditional regularity results are presented for the three-dimensional Navier-Stokes equations. The ideas are based on $L^{2m}$-norms of the vorticity, denoted by $\Omega_{m}(t)$, and particularly on $D_{m} =…

In this paper, we investigate the global regularity to 3-D inhomogeneous incompressible Navier-Stokes system with axisymmetric initial data which does not have swirl component for the initial velocity. We first prove that the $L^\infty$…

In this paper we modified the Navier-Stokes equations by adding a higher order artificial viscosity term to the conventional system. We first show that the solution of the regularized system converges strongly to the solution of the…

Smooth solutions to the axially symmetric Navier-Stokes equations obey the following maximum principle:$\|ru_\theta(r,z,t)\|_{L^\infty}\leq\|ru_\theta(r,z,0)\|_{L^\infty}.$ We first prove the global regularity of solutions if…

In this paper we introduce a probabilistic approach to show the existence of initial data with arbitrarily large $L^2(\mathbb{R}^3)$, $\dot{H}^{1/2}(\mathbb{R}^3)$ and $\mathcal{PM}^2$-norms for which a Generalized Navier-Stokes system…

This paper resolves the global regularity problem for the three-dimensional compressible magnetohydrodynamics (MHD) equations in the three-dimensional whole space, in the presence of a background magnetic field. Motivated by geophysical…

We study the motion of a particle in a random time-dependent vector field defined by the 2D Navier-Stokes system with a noise. Under suitable non-degeneracy hypotheses we prove that the empirical measures of the trajectories of the pair…

In this paper we consider the regularity problem of the Navier-Stokes equations in $ \R^{3} $. We show that the Serrin-type condition imposed on one component of the velocity $ u_3\in L^p(0,T; L^q(\R^{3} ))$ satisfying $ \frac{2}{p}+…

We investigate the long-term behavior, as a certain regularization parameter vanishes, of the three-dimensional Navier-Stokes-Voigt model of a viscoelastic incompressible fluid. We prove the existence of global and exponential attractors of…

In this article we present a Lady{\v{z}}enskaja-Prodi-Serrin Criteria for regularity of solutions for the Navier-Stokes equation in three dimensions which incorporates weak $L^p$ norms in the space variables and log improvement in the time…

Two main results will be presented in our paper. First, we will prove the regularity of solutions to axially symmetric Navier-Stokes equations under a $log$ supercritical assumption on the horizontally radial component $u^r$ and vertical…

In this paper we derive regular criteria in Lorentz spaces for Leray-Hopf weak solutions $v$ of the three-dimensional Navier-Stokes equations based on the formal equivalence relation $\pi\cong|v|^2$, where $\pi$ denotes the fluid pressure…