相关论文: A note on optimal decay rates for the axisymmetric…
We investigate the decay properties of smooth axially symmetric D-solutions to the steady Navier-Stokes equations. The achievements of this paper are two folds. One is improved decay rates of $u_{\th}$ and $\na {\bf u}$, especially we show…
We study axially symmetric $D$-solutions of three dimensional steady Navier-Stokes equations. We prove that if the velocity $u$ decays like $|x'|^{-(\frac{2}{3})^+}$ uniformly for $z$, or the vorticity $\omega$ decays like…
We study the asymptotic behavior of axisymmetric solutions with no swirl to the steady Navier-Stokes equations in the outside of the cylinder. We prove an a priori decay estimate of the vorticity under the assumption that the velocity has…
In this paper, we investigate the decay properties of axially symmetric solutions to the steady incompressible magnetohydrodynamic equations in $\mathbb{R}^3$ with finite Dirichlet integral. We first derive the decay rates of general…
We study axially symmetric D-solutions of the 3 dimensional Navier-Stokes equations. The first result is an a priori decay estimate of the velocity for general domains. The second is an a priori decay estimate of the vorticity in $\bR^3$,…
We examine the large-time behaviour of solutions to the compressible Navier-Stokes equations under the assumption of radial symmetry. In particular, we calculate a fast time-decay estimate of the norm of the nonlinear part of the solution.…
In this paper, we study the upper bound of the time decay rate of solutions to the Navier-Stokes equations and generalized Navier-Stokes equations with damping term $|u|^{\beta-1}u$ ($\beta>1$) in $\mathbb{R}^3$.
In this paper, we investigate the optimal decay rate for the higher order spatial derivative of global solution to the compressible Navier-Stokes (CNS) equations with or without potential force in three-dimensional whole space. First of…
In this paper, we investigative the large time decay and stability to any given global smooth solutions of the $3$D incompressible inhomogeneous MHD systems. We proved that given a solution $(a, u, B)$ of (\ref{mhd_a}), the velocity field…
In this paper we explore the extent to which discretely self-similar (DSS) solutions to the 3D Navier-Stokes equations with rough data almost have the same asymptotics as DSS flows with smoother data. In a previous work, we established…
We study the long-time behaviour of axisymmetric solutions without swirl for the threedimensional Navier-Stokes equations in the whole space. Assuming that the initial vorticity is sufficiently localised, we compute explicitly the leading…
We establish the time decay rates of the solution to the Cauchy problem for the compressible Navier-Stokes-Poisson system via a refined pure energy method. In particular, the optimal decay rates of the higher-order spatial derivatives of…
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 $L^\infty$…
We show that the solutions to the non-stationary Navier-Stokes equations in $R^d$, $d=2,3$ which are left invariant under the action of discrete subgroups of the orthogonal group $O(d)$ decay much faster as $|x|\to\infty$ or $ t \to\infty$…
This paper investigates the decay rates of the contact wave in one-dimensional Navier-Stokes equations. We study two cases of perturbations, with and without zero mass condition, i.e., the integration of initial perturbations is zero and…
In this paper, we study the decay rates for the global small smooth solutions to 3D anisotropic incompressible Navier-Stokes equations. In particular, we prove that the horizontal components of the velocity field decay like the solutions of…
This paper is devoted to establishing the optimal decay rate of the global large solution to compressible nematic liquid crystal equations when the initial perturbation is large and belongs to $L^1(\mathbb R^3)\cap H^2(\mathbb R^3)$. More…
By rewriting a bipolar Euler-Poisson equations with damping into an Euler equation with damping coupled with an Euler-Poisson equation with damping, and using a new spectral analysis, we obtain the optimal decay results of the solutions in…
In recent paper 5, it is shown that the upper decay rate of global solution of compressible Navier-Stokes(CNS) equations converging to constant equilibrium state $(1, 0)$ in $H^1-$norm is $(1+t)^{\frac34(\frac{2}{p}-1)}$ when the initial…
We develop the asymptotic behavior for the solutions to the stationary Navier-Stokes equation in the exterior domain of the 2D hyperbolic space. More precisely, given the finite Dirichlet norm of the velocity, we show the velocity decays to…