GLOBAL EXISTENCE OF CLASSICAL SOLUTION FOR A VISCOUS LIQUID-GAS TWO-PHASE MODEL WITH MASS-DEPENDENT VISCOSITY AND VACUUM

In this work, we obtain the global existence and uniqueness of classical solu-tions to a viscous liquid-gas two-phase model with mass-dependent viscosity and vacuum in one dimension, where the initial vacuum is allowed. We get the upper and lower bounds of gas and liquid masses n and m by the continuity methods which we use to study the compressible Navier-Stokes equations.

BLOW-UP OF CLASSICAL SOLUTIONS TO THE COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VACUUM

In this paper, we consider the formation of singularity for the classical solutions to compressible MHD equations without thermal conductivity or infinity electric conductivity when the initial data contains vacuum. We show that the life span of any smooth solution will not be extended to ∞, if the initial vacuum only appears in some local domain and the magnetic field vanishes on the interface that separates the vacuum and non-vacuum state, regardless the size of the initial data or the far field state.

Rigorous Axially Symmetric Consolidation Solution of Vacuum Combined Linear Loading Surcharge Preloading

Vacuum combined surcharge preloading is an effective method which has been used in ground treatment. This study presents the analytical solution of vertical drains with vacuum combined surcharge preloading. The surcharge was considered to be time-dependent preloading due to its reflection of the real situation.Moreover,the free strain,instead of equal strain hypothesis of the surface,was adopted for the mathematical rigor. Both vertical and horizontal drainages,along with the well resistance were considered.Besides,the time-dependent surcharge preloading was resolved with the impulse theorem which has been presented in the study,and the solutions for pore water pressure and degree of consolidation were derived by applying the approach of separation of variables.Furthermore,the solution is compared with previous solutions and numerical solutions,and the results verify the correctness of the proposed model.

GLOBAL STRONG SOLUTION AND EXPONENTIAL DECAY OF 3D NONHOMOGENEOUS ASYMMETRIC FLUID EQUATIONS WITH VACUUM

We prove the global existence and exponential decay of strong solutions to the three-dimensional nonhomogeneous asymmetric fluid equations with nonnegative density provided that the initial total energy is suitably small.Note that although the system degenerates near vacuum,there is no need to require compatibility conditions for the initial data via time-weighted techniques.

Local Strong Solutions for the Cauchy Problem of 2D Density-Dependent Boussinesq Equations with Vacuum

The main goal of the paper is to obtain the local strong solution of the Cauchy problem of the nonhomogeneous incompressible Boussinesq equation in two-dimension space. Especially, when the far-field density is vacuum, we make a priori estimate in a bound ball and prove the existence and uniqueness of the local strong solution of the Boussinesq equation.

Vacuum Solutions of Classical Gravity on Cyclic Groups from Noncommutative Geometry

Based on the observation that the moduli of a link variable on a cyclic group modify Connes' distance on this group, we construct several action functionals for this link variable within the framework of noncommutative geometry. After solving the equations of motion, we find that one type of action gives nontrivial vacuum solution for gravity on this cyclic group in a broad range of coupling constants and that such a solution can be expressed with Chebyshev's polynomials.

ON THE EXISTENCE OF LOCAL CLASSICAL SOLUTION FOR A CLASS OF ONE-DIMENSIONAL COMPRESSIBLE NON-NEWTONIAN FLUIDS

In this paper, the aim is to establish the local existence of classical solutions for a class of compressible non-Newtonian fluids with vacuum in one-dimensional bounded intervals, under the assumption that the data satisfies a natural compatibility condition. For the results, the initial density does not need to be bounded below away from zero.

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.

STRONG SOLUTIONS FOR THE INCOMPRESSIBLE FLUID MODELS OF KORTEWEG TYPE

In this article, we are concerned with the strong solutions for the incompress- ible fluid models of Korteweg type in a bounded domain Ω СR^3. We prove the existence and uniqueness of local strong solutions to the initial boundary value problem. We point out that in this article we allow the existence of initial vacuum provided initial data satisfy a compatibility condition.

A STRONG SOLUTION OF NAVIER-STOKES EQUATIONS WITH A ROTATION EFFECT FOR ISENTROPIC COMPRESSIBLE FLUIDS

We study the initial boundary value problem for the three-dimensional isentropic compressible Navier-Stokes equations in the exterior domain outside a rotating obstacle,with initial density having a compact support.By the coordinate system attached to the obstacle and an appropriate transformation of unknown functions,we obtain the three-dimensional isentropic compressible Navier-Stokes equations with a rotation effect in a fixed exterior domain.We first construct a sequence of unique local strong solutions for the related approximation problems restricted in a sequence of bounded domains,and derive some uniform bounds of higher order norms,which are independent of the size of the bounded domains.Then we prove the local existence of unique strong solution of the problem in the exterior domain,provided that the initial data satisfy a natural compatibility condition.

THE GLOBAL EXISTENCE OF STRONG SOLUTIONS TO THE 3D COMPRESSIBLE ISOTHERMAL NAVIER-STOKES EQUATIONS

This paper concerns the global existence of strong solutions to the 3 D compressible isothermal Navier-Stokes equations with a vacuum at infinity.Based on the special structure of the Zlotnik inequality,the time uniform upper bounds for density are established through some time-dependant a priori estimates under the assumption that the total mass is suitably small.

Global Existence and Large Time Asymptotic Behavior of Strong Solution to the Cauchy Problem of 2D Density-Dependent Boussinesq Equations of Korteweg Type

In this paper, we study the Cauchy problem of the density-dependent Boussinesq equations of Korteweg type on the whole space with a vacuum. It is proved that there exists a unique strong solution for the two-dimensional Cauchy problem established that the initial density and the initial temperature decay not extremely slow. Particularly, it is allowed to be arbitrarily large for the initial data and vacuum states for the initial density, even including the compact support. Moreover, when the density depends on the Korteweg term with the viscosity coefficient and capillary coefficient, we obtain a consistent priority estimate by the energy method, and extend the local strong solutions to the global strong solutions. Finally, when the pressure and external force are not affected, we deform the fluid models of Korteweg type, we can obtain the large time decay rates of the gradients of velocity, temperature and pressure.

COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH DENSITY-DEPENDENT VISCOSITY,VACUUM AND GRAVITATIONAL FORCE IN THE CASE OF GENERAL PRESSURE

This is a continuation of the article（Comm.Partial Differential Equations 26（2001）965）.In this article,the authors consider the one-dimensional compressible isentropic Navier-Stokes equations with gravitational force,fixed boundary condition,a general pressure and the density-dependent viscosity coefficient when the viscous gas connects to vacuum state with a jump in density.Precisely,the viscosity coefficient μ is proportional to ρ^θ and 0〈θ〈1/2,where ρ is the density,and the pressure P=P（ρ）is a general pressure.The global existence and the uniqueness of weak solution are proved.

Application of Vacuum Drying to Silica Sol Ceramic Mold

Silica sol ceramic mold was made at room temperature with JN-30 silica sol, silica powder and NH4Cl. It is found that the harden time of silica sol ceramic mold is only 0.5 to 1.5 h under the amount of NH4Cl solution of 7% to 8% with 15% concentration, and less surface cracks occur by using vacuum drying. The proper vacuum drying process parameters： vacuum drying temperature is 80 to 100℃, drying time is 5 h and vacuum is 0.06 to 0.07MPa. The harden mechanics, vacuum drying mechanics and the reason of less surface cracks of silica sol ceramic mold by vacuum drying： were also analyzed in this paper.

Prediction to the Efficiency of Soft Clay Sample Preparation with Vacuum Loading

Vacuum loading has been examined as a way of preparing uniformly consolidated soft clay samples. The facility and loading procedure are described in this paper. An analytical solution to the three dimensional consolidation equation is derived for estimating the degree of consolidation of the soil sample with vacuum loading. The given example shows that the predicted degree of consolidation of a soft clay bulk with vacuum loading is close to that measured in the consolidation process.

THE LOCAL WELL-POSEDNESS OF A CHEMOTAXIS-SHALLOW WATER SYSTEM WITH VACUUM

In this paper we prove the local well-posedness of strong solutions to a chemotaxisshallow water system with initial vacuum in a bounded domainΩ■R^(2)without the standard compatibility condition for the initial data.This improves some results obtained in[J.Differential Equations 261(2016),6758-6789].

Resolving the Vacuum Catastrophe: A Generalized Holographic Approach

We address the ~122 orders of magnitude discrepancy between the vacuum energy density at the cosmological scale and the vacuum density predicted by quantum field theory. This disagreement is known as the cosmological constant problem or the “vacuum catastrophe”. Utilizing a generalized holographic model, we consider the total mass-energy density in the geometry of a spherical shell universe (as a first order approximation) and find an exact solution for the currently observed critical density of the universe. We discuss the validity of such an approach and consider its implications to cosmogenesis and universal evolution.

等应变条件下增压式真空预压固结解析解

从注气增压对土体作用效果的角度出发,建立增压式真空预压固结解析理论模型。提出基于注气增压压力等效的受力简化模型;引入新参数——径向渗透系数增大系数η,反映注气过程对土体渗透性质的改变。根据Barron等应变假定和达西定律,考虑排水板涂抹效应与井阻作用、土体径-竖向渗流以及上部堆载,推导增压式真空预压固结控制方程及其解析解,并利用弹性力学方法推导等效注气增压压力p(t)的计算公式。针对瞬时增压和线性增压两种特例给出具体解析解公式,并通过与工程案例对比分析,验证了解析解及等效力计算方法的合理性。通过对固结性状的分析得出如下结论:注气增压方法可增大土体负孔隙水压力值,加速土体排水固结;“参数η”对固结速率的影响较大,分析模型中考虑注气过程对径向渗透系数的改变会更加合理;井阻作用会导致土体固结速率减慢,径-竖向渗流时孔压能够消散完成,而只有径向渗流时孔压无法消散完成。

Microstructure and properties of Cu-0.6Cr alloy after vacuum continuous casting

To promote the solution of chromium in copper and the purity of copper-chromium(Cu-Cr) alloy,vacuum continuous casting(VCC) process was employed to fabricate the Cu-Cr alloy required for electrode material. Cu-0.6Cr(containing 0.6%(mass fraction) chromium) alloy bar with a diameter of 12 mm was cast with a constant rate of 250 mm/min. The microstructure,mechanical properties,and physical properties were discussed. After solid solution strengthening and aging treatments,Cu-0.6Cr alloy fabricated by VCC process has higher tensile strength(σ≥314 MPa),elongation rate(δ≥34%),conductivity(≥80.5% IACS),and hardness(80 HRB) compared to the as-cast alloy.