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.

Isotherm Equation Study of F Adsorbed from Water Solution by Fe2（SO4）3-modified Granular Activated Alumina

The adsorption equilibrium of a fluoride solution on 1-2 mm granular activated alumina modified by Fe2(SO4)3 solution was investigated.The experiments were conducted using a wide range of initial fluoride concentrations(0.5 to 180 mg·L-1 at pH～7.0) and an adsorbent dose of 1.0 g·L-1.The application of Langmuir and Freundlich adsorption isotherm models(linear and nonlinear forms) generally showed that a single Langmuir or Freundlich equation cannot fit the entire concentration gap.Experimental data on low equilibrium concentrations(0.1 to 5.0 mg·L-1) was in line with both Langmuir and Freundlich isotherm models,whereas that of high equilibrium concentrations(5.0 to 150 mg·L-1) was more in line with the Freundlich isotherm model.A new LangmuirFreundlich function was used for the entire concentration gap,as well as for low and high concentrations.

Adsorption Kinetics of NH_4^+ by Purple Soils with Different pH Values

Ammonium adsorption and desorption properties by purple soils with dif- ferent pH were studied. The results showed that the adsorption and desorption amounts of NH4＋ by purple soils increased with the increase of NH4＋ concentration, regardless of soil pH values; the largest adsorption and desorption amounts of NH4＋ by purple soil at pH 6.0 were 10.3 and 7.96 mg/g, respectively; the largest adsorp- tion and desorption amounts of NH4＋ by purple soil at pH 7.2 were 12.8 and 4.62 mg/g, respectively; the largest adsorption and desorption amounts of NH4＋ by purple soil at pH 8.0 were 13.5 and 2.23 mg/g, respectively. The isothermal adsorption ki- netics of NH4＋ by purple soils fits the Freundlich equation best （R〉0.95）. This study shows that the adsorption of NH4＋ by purple soils with different pH values is multi- molecular layer uneven surface adsorption.

H^2-Stabilization of the Isothermal Euler Equations: a Lyapunov Function Approach

The authors consider the problem of boundary feedback stabilization of the 1D Euler gas dynamics locally around stationary states and prove the exponential stability with respect to the H2-norm. To this end, an explicit Lyapunov function as a weighted and squared H2-norm of a small perturbation of the stationary solution is constructed. The authors show that by a suitable choice of the boundary feedback conditions, the H2- exponential stability of the stationary solution follows. Due to this fact, the system is stabilized over an infinite time interval. Furthermore, exponential estimates for the C norm are derived.

Analogy between adsorption and sorption： An elementary mechanistic approach. I. Monolayer adsorption and sorption without solvent cluster formation

The elementary mechanistic model of adsorption and sorption is based on a simple hypothesis： the adsorption sites are uniformly distnbuted on the surface of the pore walls in the adsorbent, the sorption sites are uniformly distributed in the volume of the polymer. In this first paper we will analyze the simple case where one solute molecule is only allowed to occupy a single adsorption or sorption site. A common elementary occupation law of the free sites is assumed： the differential increase of the number of the adsorbed/sorbed molecules is proportional to the differential increase of the activity of the solute and the concentration of the free （non-occupied） sites in the solid. The proportionality coefficient is called affinity coefficient depending on the solid/solute couple and on the temperature and independent of the concentration of the solute. In adsorption the concentration of the free sites is a surface concentration on the pore walls and in sorption it is expressed by the molarity. The simple monolayer adsorption law of Jovanovic is obtained： n = no（1 - e KP） where n is the number of moles adsorbed when the pressure is P. no is the total number of adsorption sites and K the affinity coefficient for adsorption. The sorption law writes： a = 1/k [Ф/1-Ф] ＋ 1-r/k In [1 ＋ 1/r Ф/1-Ф] where Ф, r and k hold respectively for the volume fraction of the solvent in the polymer, for the ratio of the molar volumes of the solvent to the elementary polymer chain containing one single adsorption site and for the sorption affinity coefficient. The confrontation of these equations to experimental isotherms is satisfactory in comparison with the classical Langmuir and Flory-Huggins equations： the best results are obtained for adsorption of vapors on a 5A zeolite and for all analyzed sorption results.

Local well-posedness of a multidimensional shock wave for the steady supersonic isothermal flow

In this paper, we prove the local existence, uniqueness and stability of a supersonic shock for the supersonic isothermal incoming flow past a curved cone. Major difficulties include constructing an appropriate solution and treatincg the Neumann boundary conditions and local stability condition.