相关论文: Space-time decay of Navier-Stokes flows invariant …

In this paper we describe a method to derive classical solutions of the Navier-Stokes equations for non-stationary initial value problems in domain R^n (n = 2, 3 or higher). A new closed-form analytic solution of the incompressible…

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 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…

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…

The paper studies the issue of stability of solutions to the Navier-Stokes and damped Euler systems in periodic boxes. We show that under action of fast oscillating-in- time external forces all two dimensional regular solutions converge to…

We show that, for a given H\"older continuous curve in $\{(\gamma(t),t)\,:\, t>0\} \subset R^3\times R^+$, there exists a solution to the Navier-Stokes system for an incompressible fluid in $R^3$ which is smooth outside this curve and…

In this paper, we investigate the convergence of the global large solution to its associated constant equilibrium state with an explicit decay rate for the compressible Navier-Stokes equations in three-dimensional whole space. Suppose the…

A well-known unsolved problem (in the classical theory of fluid mechanics) is to identify a set of initial velocities, which may depend on the viscosity, the body forces and possibly the boundary of the fluid that will allow global in time…

In this paper, we present a refined framework for the global-in-time well-posedness theory for the pressureless Euler--Navier--Stokes system and the optimal temporal decay rates of certain norms of solutions. Here the coupling of two…

In this paper, we study the decay rate of the Stokes flow in an exterior domain with a slowly decaying initial data ${\bf u}_0(x)=O(|x|^{-\al}), 0<\al\leq n$. %which is not $L^1$ integrable. As an application we find the unique strong…

We prove the existence of small amplitude, time-quasi-periodic solutions (invariant tori) for the incompressible Navier-Stokes equation on the $d$-dimensional torus $\T^d$, with a small, quasi-periodic in time external force. We also show…

We consider weak (''Leray'') solutions to the stationary Navier-Stokes system with Oseen and rotational terms, in an exterior domain. It is shown the velocity may be split into a constant times the first column of the fundamental solution…

We first prove decay estimates and spacetime integral bounds for Stokes flows in amalgam spaces $E^r_q$ which connect the classical Lebesgue spaces to the spaces of uniformly locally $r$-integrable functions. Using these estimates, we…

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 study the long-time behavior of a point mass moving in a one-dimensional viscous compressible fluid. Previously, we showed that the velocity of the point mass $V(t)$ satisfies a decay estimate $V(t)=O(t^{-3/2})$~[K. Koike, J.…

Consider the Navier-Stokes flow past a rotating obstacle with a general time-dependent angular velocity and a time-dependent outflow condition at infinity. After rewriting the problem on a fixed domain, one obtains a non-autonomous system…

The aim of this paper is to show time-decay estimates of solutions to linearized two-phase Navier-Stokes equations with surface tension and gravity. The original two-phase Navier-Stokes equations describe the two-phase incompressible…

In this small note we strengthen the classic result about the regularity time t* of arbitrary Leray solutions to the (incompressible) Navier-Stokes equations in Rn (n = 3, 4), which have the form: t* <= K_{3} nu^{-5} || u(.,0) ||_{L2}^{4}…

Both experimental and numerical studies of fluid motion indicate that initially localized regions of vorticity tend to evolve into isolated vortices and that these vortices then serve as organizing centers for the flow. In this paper we…

We investigate analytically and numerically the existence of stationary solutions converging to zero at infinity for the incompressible Navier-Stokes equations in a two-dimensional exterior domain. More precisely, we find the asymptotic…