Trilinear Lp estimates with applications to the Cauchy problem for the Hartree-type equation

In this paper, $L^p$ estimates for a trilinear operator associated with the Hartree type nonlinearity are proved. Moreover, as application of these estimates, it is proved that after a linear transformation, the Cauchy problem for the Hartree-type equation becomes locally well posed in the Bessel potential and homogeneous Besov spaces under certain regularity assumptions on the initial data. This notion of well-posedness and the functional framework to solve the equation were firstly proposed by Y. Zhou.     

变角度纤维复合材料层合斜板的颤振分析

假设纤维方向角沿层合板的长度方向线性变化，研究了变角度纤维复合材料层合斜板的颤振．通过坐标变换将斜板变换为正方形板，采用层合板表面连续变化的速度环量来模拟空气对其的作用，速度环量分布利用Cauchy积分公式计算．建立了系统的Lagrange方程并采用Ritz法得到了层合板的自振频率和颤振/不稳定性分离临界速度．通过数值算例验证了本文模型和方法的正确性和收敛性，分析了各个铺层内纤维方向角的变化对自振频率和颤振/不稳定性分离临界速度的影响．研究结果表明，通过纤维的变角度铺设，可有效地提高层合板的基频和颤振/不稳定性分离临界速度．经合理设计的变角度复合材料层合板具有抑制颤振的作用．     

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In this paper, the asymptotic behavior of the weak solution (u_t)_{t\ge0} to the non-local Cauchy problems as stated in (1) is considered. Only using lower bounds of jumping kernel J(x,y) for large |x-y|, it is obtained that \|u_t\|_p\le c(t)\|u_0\|_q with any 1\le q相似文献   

The Shakhov model near a global Maxwellian

Shakhov model is a relaxation approximation of the Boltzmann equation proposed to overcome the deficiency of the original BGK model, namely, the incorrect production of the Prandtl number. In this paper, we address the existence and the asymptotic stability of the Shakhov model when the initial data is a small perturbation of global equilibrium. We derive a dichotomy in the coercive estimate of the linearized relaxation operator between zero and non-zero Prandtl number, and observe that the linearized relaxation operator is more degenerate in the former case. To remove such degeneracy and recover the full coercivity, we consider a micro–macro system that involves an additional non-conservative quantity related to the heat flux.     

A STABILITY STUDY OF NAVIER-STOKES EQUATIONS (Ⅲ)

ＡＳＴＡＢＩＬＩＴＹＳＴＵＤＹＯＦＮＡＶＩＥＲ－ＳＴＯＫＥＳＥＱＵＡＴＩＯＮＳ（Ⅲ）ＳｈｉＷｅｉ－ｈｕｉ（施惟慧）（ｓｈａｎｇｈａｉＵｎｉｖｅｒｓｉｌｙ．Ｓｈａｎｇｈａｉ）（ＲｅｃｅｉｖｅｄＪａｎ．２０．１９９４；ＣｏｍｍｕｎｉｃａｔｅｄｂｙＣｈｉｅ...     

Poincaré Mapping Method for Hydrodynamic Systms. Dynamic Chaos in a Fluid Layer between Eccentrically Rotating Cylinders

Investigation of the plane–parallel motion of particles of an incompressible medium reduces to investigation of a Hamiltonian system. The Hamiltonian function is a stream function. The timeperiodic mixing of an incompressible medium is described by a timeperiodic Hamiltonian function. The mixing of the medium is associated with dynamic chaos. Transition to dynamic chaos is studied by analysis of the positions of Lagrangian particles at times divisible by the period — Poincaré recurrence points. The set of Poincaré recurrence points is studied with the use of Poincaré mapping on the phase flow. A method for constructing Poincaré maps in parametric form is proposed. A map is constructed as a series in a small parameter. It is shown that the parametric method has a number of advantages over the generating function method is shown. The proposed method is used to examine the motion of particles of an incompressible viscous fluid layer between two circular cylinders. The outer cylinder is immovable, and the inner cylinder rotates about a point that does not coincide with the centers of both cylinders. An optimal mode for the motion is established, in which the area of the chaotic region is maximal.