Global Classical Solutions for One Dimensional Navier Stokes Equations

In this article the author considers Cauchy problem for one dimensional Navier Stokes equations and the global smooth resolvablity for classical solutions is obtained.

EXISTENCE AND UNIQUENESS OF THE WEAK SOLUTION TO THE INCOMPRESSIBLE NAVIER-STOKES-LANDAU-LIFSHITZ MODEL IN 2-DIMENSION

In this paper, we prove the existence and uniqueness of the weak solution to the incompressible Navier-Stokes-Landau-Lifshitz equations in two-dimension with finite energy.The main techniques is the Faedo-Galerkin approximation and weak compactness theory.

THE FUNDAMENTAL SOLUTION METHOD FOR INCOMPRESSIBLE NAVIER STOKES EQUATIONS

A complete boundary integral formulation for incompressible Navier Stokes equations with time discretization by operator splitting is developed by using the fundamental solutions of the Helmhotz operator equation with different orders. The numerical results for the lift and the drag hysteresis associated with a NACA0012 aerofoil oscillating in pitch are good in comparison with available experimental data.

GLOBAL WEAK SOLUTION TO COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY,VACUUM AND GRAVITATIONAL FORCE

Recently,the global existence of weak solutions to the compressible Navier-Stokes equations with vacuum has attracted much attention.In this paper,we study the one-dimension isentropic Navier-Stokes equations with gravitational force and fixed boundary condition when the density connects with vacuum discontinuously.We prove the global existence and the uniqueness of weak solution,requiring less regularity of the initial data.

On Partial Regularity of Suitable Weak Solutions to the Stationary Fractional Navier-Stokes Equations in Dimension Four and Five

In this paper, we investigate the partial regularity of suitable weak solutions to the multi- dimensional stationary Navier-Stokes equations with fractional power of the Laplacian （-△）^α （n/6 ≤α〈1 and a ≠ 1/2）. It is shown that the n ＋ 2 - 6α （3 ≤ n ≤5） dimensional Hausdorff measure of the set of the possible singular points of suitable weak solutions to the system is zero, which extends a recent result of Tang and Yu [19] to four and five dimension. Moreover, the pressure in ε-regularity criteria is an improvement of corresponding results in [1, 13, 18, 20].

NEW PROOFS OF THE DECAY ESTIMATE WITH SHARP RATE OF THE GLOBAL WEAK SOLUTION OF THE n-DIMENSIONAL INCOMPRESSIBLE NAVIER-STOKES EQUATIONS

Consider the Cauchy problem for the n-dimensional incompressible NavierStokes equations:??tu-α△u+(u·?)u+?p = f(x, t), with the initial condition u(x, 0) = u_0(x) and with the incompressible conditions ? · u = 0, ? · f = 0 and ? · u_0= 0. The spatial dimension n ≥ 2.Suppose that the initial function u_0∈ L1(Rn) ∩ L^2(Rn) and the external force f ∈ L^1(Rn× R+) ∩ L^1(R+, L^2(Rn)). It is well known that there holds the decay estimate with sharp rate:(1 + t)1+n/2∫Rn|u(x, t)|2 dx ≤ C, for all time t > 0, where the dimension n ≥ 2, C > 0 is a positive constant, independent of u and(x, t).The main purpose of this paper is to provide two independent proofs of the decay estimate with sharp rate, both are complete, systematic, simplified proofs, under a weaker condition on the external force. The ideas and methods introduced in this paper may have strong influence on the decay estimates with sharp rates of the global weak solutions or the global smooth solutions of similar equations, such as the n-dimensional magnetohydrodynamics equations, where the dimension n ≥ 2.

WEAK TIME-PERIODIC SOLUTIONS TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS

The compressible Navier-Stokes equations driven by a time-periodic external force are considered in this article. We establish the existence of weak time-periodic solutions and improve the result from [3] in the following sense： we extend the class of pressure functions, that is, we consider lower exponent γ.

EXISTENCE AND UNIQUENESS OF WEAK SOLUTIONS FOR TWO-DIMENSIONAL MODIFIED NAVIER-STOKES EQUATIONS

This paper studies a two-dimensional modified Navier-stokes equations. The author shows the existence and uniqueness of weak solutions for this equation by Galerkin method in bounded domains. The result is further extended to the case of unbounded channel-like domains.

分数阶不可压缩Navier-Stokes方程解的爆破性准则

采用Fourier分析及其标准技巧,研究分数阶不可压缩Navier-Stokes方程在齐次Sobolev-Gevrey空间H_(a,σ)^(s)(R^(3))(a>0,σ>1,5/2-2α<s<3/2,1≤α≤5/4)中的初值问题.首先证明当初值u_(0)∈H_(a,σ)^(s)(R^(3))方程存在唯一解u∈C(0,T*);H_(a,σ)^(s)(R^(3));其次证明当T*<∞时,解的指数型爆破准则.

平坦环上受迫Navier-Stokes方程的几乎周期响应解

本文证明了平坦环T_(Γ)^(d)上几乎周期的小外力作用下的不可压Navier-Stokes方程存在小振幅的几乎周期响应解.

二维不可压缩Navier-Stokes-Landau-Lifshitz方程组的全局强解

本文在二维光滑有界区域中研究不可压缩的Navier-Stokes-Landau-Lifshitz方程组的初边值问题.在初始密度包含真空的情况下,证明在具有任意大的初始速度以及初始时刻宏观分子取向力梯度变化适当小的条件下,该问题全局强解的存在唯一性.

一维可压缩Navier-Stokes方程组弱解的能量守恒

本文主要研究的是对任意的t>0,一维周期区域中可压缩Navier-Stokes方程组的弱解在某种特定的条件下满足能量守恒.具体来说,通过运用交换子估计的方法以及使弱解满足某种足够的正则性条件,从而可以得到在一维周期区域中弱解满足相应的能量等式.

时空分数阶Navier-Stokes方程解的存在性

本文研究了时空分数阶不可压缩Navier-Stokes方程的Cauchy问题,并在Marcinkiewicz空间中建立了该方程mild解的存在唯一性.具体地,利用Mittag-Leffler算子在Marcinkiewicz空间的弱L^(r)-弱L^(q)估计以及关于时间的连续性和不动点定理,在BC((0,∞);L_(σ)^(d/α-1,∞)(R^(d)))空间得到了小初值条件下该方程的全局mild解的存在唯一性.

ON THE EXISTENCE AND UNIQUENESS OF THE SOLUTION TO THE NAVIER－STOKES EQUATIONS

In this paper we discuss the mixed boundary problem (1)-(3) of the NavierStokes equations for the flow of an incompressible viscous fluid in a bounded domain. we prove that when g,and,there exists a weak solution of (1)-(3),and when u,the weak solution is unique,if it exists.

TIME PERIODIC SOLUTION TO THE COMPRESSIBLE NAVIER-STOKES EQUATIONS IN A PERIODIC DOMAIN

This article is concerned with the time periodic solution to the isentropic compressible Navier-Stokes equations in a periodic domain. Using an approach of parabolic regularization, we first obtain the existence of the time periodic solution to a regularized problem under some smallness and symmetry assumptions on the external force. The result for the original compressible Navier-Stokes equations is then obtained by a limiting process. The uniqueness of the periodic solution is also given.

GLOBAL CLASSICAL SOLUTION TO THE CAUCHY PROBLEM OF THE 3-D COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY

In this paper, we consider the global existence of classical solution to the 3-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient λ(ρ)provided that the initial energy is small in some sense. In our result, we give a relation between the initial energy and the viscosity coefficient μ, and it shows that the initial energy can be large if the coefficient of the viscosity μ is taken to be large, which implies that large viscosity μ means large solution.

GLOBAL EXISTENCE OF STRONG SOLUTIONS OF NAVIER-STOKES EQUATIONS WITH NON-NEWTONIAN POTENTIAL FOR ONE-DIMENSIONAL ISENTROPIC COMPRESSIBLE FLUIDS

The aims of this paper are to discuss global existence and uniqueness of strong solution for a class of isentropic compressible navier-Stokes equations with non-Newtonian in one-dimensional bounded intervals. We prove two global existence results on strong solutions of isentropic compressible Navier-Stokes equations. The first result shows only the existence. And the second one shows the existence and uniqueness result based on the first result, but the uniqueness requires some compatibility condition.

GLOBAL CLASSICAL SOLUTIONS TO THE 3-D ISENTROPIC COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH GENERAL INITIAL ENERGY

We establish the global existence and uniqueness of classical solutions to the Cauchy problem for the 3-D compressible Navier-Stokes equations under the assumption that the initial density ｜｜po｜｜L∞ is appropriate small and 1 〈 γ 〈 6/5. Here the initial density could have vacuum and we do not require that the initial energy is small.

STRONG SOLUTIONS OF THE COUPLED NAVIER-STOKES-POISSON EQUATIONS FOR ISENTROPIC COMPRESSIBLE FLUIDS

In this article, we are concerned with the strong solutions of the coupled Navier-Stokes-Poisson equations for isentropic compressible fluids in a domain Ω R^3. We prove the local existence of unique strong solutions provided that the initial data u0 and u0 satisfy a nature compatibility condition. The important point in this article is that we allow the initial vacuum： the initial density may vanish in an open subset of Ω. This is achieved by getting some uniform estimates and using a Schauder fixed point theorem.

ON THE FORMAL SOLUTION OF INITIAL VALUE PROBLEM OF NAVIER-STOKES EQUATION

A necessary and sufficient conditions of the existence of formal solution to the initial value problem of Navier-Stokes equation an R-3 x R are presented. A computation case is also given.