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1.
We consider the defocusing, -critical Hartree equation for the radial data in all dimensions (n5). We show the global well-posedness and scattering results in the energy space. The new ingredient in this paper is that we first take advantage of the term in the localized Morawetz identity to rule out the possibility of energy concentration, instead of the classical Morawetz estimate dependent of the nonlinearity.  相似文献
2.
一类广义层流方程组的初值问题的局部适定性   总被引:1,自引:0,他引:1       下载免费PDF全文
讨论层流理论中描述比重相近的层流间相互作用的方程组的方程组的广义方程级,通过引进一类函数空间和一系列先验估计,应用不动点原理,分别得到该类广义层流方程组的初值问题在H∧s(R),s≥1的局部适定性。  相似文献
3.
基于人工压缩性方法提出一中心与迎风混合的算法,以数值模拟N-S方程的定常/非定常解,对半离散方程的左端采用中心差分,方程右端数值流量采用迎风Roe近似算法,其精度可达三阶.湍流模式利用Baldwin-Lomax代数模式。计算例子包括二维平板、机翼剖面、扁椭球、颅动脉瘤等。计算结果表明,压力和摩擦系数与实验符合,在分离涡旋区计算值与实验有差别,这或许是由于湍流模式不够精确的缘故。  相似文献
4.
We prove that the Korteweg–de Vries initial-value problem is globally well-posed in and the modified Korteweg–de Vries initial-value problem is globally well-posed in . The new ingredient is that we use directly the contraction principle to prove local well-posedness for KdV equation in H−3/4 by constructing some special resolution spaces in order to avoid some ‘logarithmic divergence’ from the high–high interactions. Our local solution has almost the same properties as those for Hs (s>−3/4) solution which enable us to apply the I-method to extend it to a global solution.  相似文献
5.
6.
The object of this article is to study the boundary layer appearing at large Reynolds number (small viscosity ε) incompressible Navier-Stokes Equation in a cylinder in space dimension three. These are Navier-Stokes equations linearized around a fixed velocity flow: the authors study the convergence as ε→0 to the inviscid type equations, the authors define the correctors needed to resolve the boundary layer and obtain convergence results valid up to the boundary and the authors also study the behavior of the boundary layer when, simultaneously, time and the Reynolds number tend to infinity, in which case the boundary layer tends to pervade the whole domain.  相似文献
7.
We propose and study a class of generalized surface quasi-geostrophic equations. We show that in the inviscid case certain radial solutions develop gradient blow-up in finite time. In the critical dissipative case, the equations are globally well-posed with arbitrary initial data.

  相似文献

8.
A relaxation system based on a Lattice-Boltzmann type discrete velocity model is considered in the low Mach number limit. A third order relaxation scheme is developed working uniformly for all ranges of the mean free path and Mach number. In the incompressible Navier-Stokes limit the scheme reduces to an explicit high order finite difference scheme for the incompressible Navier-Stokes equations based on nonoscillatory upwind discretization. Numerical results and comparisons with other approaches are presented for several test cases in one and two space dimensions.

  相似文献

9.
We prove low regularity global well-posedness for the 1d Zakharov system and the 3d Klein-Gordon-Schrödinger system, which are systems in two variables and . The Zakharov system is known to be locally well-posed in and the Klein-Gordon-Schrödinger system is known to be locally well-posed in . Here, we show that the Zakharov and Klein-Gordon-Schrödinger systems are globally well-posed in these spaces, respectively, by using an available conservation law for the norm of and controlling the growth of via the estimates in the local theory.

  相似文献

10.
We prove that the Benjamin-Ono initial-value problem is globally well-posed in the Banach spaces , , of real-valued Sobolev functions.

  相似文献

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