Takaaki Nishida

Initial-boundary value problems for the equations of motion of compressible viscous and heat-conductive fluids

The equations of motion of compressible viscous and heat-conductive fluids are investigated for initial boundary value problems on the half space and on the exterior domain of any bounded region. The global solution in time is proved to exist uniquely and approach the stationary state ast→∞, provided the prescribed initial data and the external force are sufficiently small.

Fluid dynamical limit of the nonlinear Boltzmann equation to the level of the compressible Euler equation

The nonlinear Boltzmann equation for a rarefied gas is investigated in the fluid dynamical limit to the level of compressible Euler equation locally in time, as the mean free path ε tends to zero. The nonlinear hyperbolic conservation laws obtained as the limit are also the first approximation of the Chapman-Enskog expansion.

On the fluid-dynamical approximation to the Boltzmann equation at the level of the Navier-Stokes equation

The compressible and heat-conductive Navier-Stokes equation obtained as the second approximation of the formal Chapman-Enskog expansion is investigated on its relations to the original nonlinear Boltzmann equation and also to the incompressible Navier-Stokes equation. The solutions of the Boltzmann equation and the incompressible Navier-Stokes equation for small initial data are proved to be asymptotically equivalent (mod decay ratet−5/4) ast→+∞ to that of the compressible Navier-Stokes equation for the corresponding initial data.

Mixed problems for nonlinear conservation laws

We consider the mixed problem for the system of equations wt u, = 0, Uf + P(4, = 0, (1) where p(g) = K2v-y, y = 1 + 2~, E > 0, K = const > 0, in regions (a) x > 0, t > 0, and in regions (b) 0 0. In both cases we prescribe initial data (4x, Oh 4x, 0)) = (~“(4 %(X)h (2) where 0 , t >, 0, (3) while in regions (b) we prescribe boundary data (3) and

Large-Time Behavior of Viscous Surface Waves.

Publisher Summary This chapter discusses the large-time behavior of viscous surface waves. It presents global in time solutions to a free surface problem of the viscous incompressible fluid, which is formulated as the motion of the fluid, governed by the Navier–Stokes equation.

On the Broadwell model of the Boltzmann equation for a simple discrete velocity gas

The Broadwell model of the Boltzmann equation for a simple discrete velocity gas is investigated on two asymptotic problems. (a) The decay of solutions inx∈R ast→+∞. (b) The hydrodynamical limit in the compressible Euler level as the mean free path∈→0.

Equations of Motion of Compressible Viscous Fluids

Abstract We survey the global solutions of equations for one-dimensional motion of compressible, viscous and heat-conductive fluids. Initial value problems with fixed and free boundaries are treated about solutions global in time and about the asymptotic behaviors as time tends to infinity.

Belowground microbial symbiont enhances plant susceptibility to a spider mite through change in soybean leaf quality.

To examine how rhizobia affect the chemical and nutrient status in leaves of soybean (Glycine max L.), and how rhizobia change plant susceptibility to a generalist spider mite (Tetranycus urticae), we cultivated root-nodulating soybeans (R+) and their non-nodulating mutant (R−) in a common garden. We experimentally fertilized the plants with nitrogen to examine effects of rhizobia on the plant traits and plant susceptibility to spider mites at different nitrogen levels. R+ plants produced more leaves containing greater nitrogen and less total phenolics than R− plants. Spider mites fed on R+ leaves produced more eggs than those fed on R− leaves. The positive effect of rhizobia on spider mite fecundity could be due to an increase in foliar N content and/or to a decrease in concentration of phenolics. Although root nodule mass did not differ among different nitrogen levels, ureide-N, an indicator of nitrogen provided by rhizobia, in xylem sap decreased at moderate and high soil nitrogen levels. Therefore, we expected that rhizobia effects on egg production of the spider mite would decrease in high soil nitrogen conditions. However, the effect of rhizobia was still maintained even at high soil nitrogen levels. Thus, soil nitrogen and rhizobia may independently affect the reproductive performance of the spider mite.

Arbuscular mycorrhizal fungi species-specifically affect induced plant responses to a spider mite

It is widely recognized that arbuscular mycorrhizal fungi (AMF) improve plant growth and nutrient conditions, but their effects can vary from negative to positive depending on AMF species. Since the performance of herbivorous arthropods varies with plant quality, different AMF species should differently affect the density of herbivorous arthropods on plants and the herbivore-induced plant responses. We examined the indirect effects of AMF on the number of spider mites (Tetranychus urticae) and the number of damaged leaves in an outdoor glass-chamber experiment, using Lotus japonicus plants inoculated with one of four different AMF species (Gigaspora margarita, Glomus etunicatum, Gl. intraradices, and Acaulospora longula). Plants with Gi. margarita and A. longula had significantly fewer female mites than plants with Gl. etunicatum and Gl. intraradices, and plants with Gi. margarita had the fewest damaged leaves, followed by plants with A. longula,Gl. intraradices, and Gl. etunicatum. To examine species-specific effects of AMF on herbivore-induced plant responses, we carried out a bioassay with eggs laid by spider mites, and analyses of leaf chemicals (carbon, nitrogen, phosphorus, and total phenolics) using plants subjected or not subjected to herbivory. The bioassay showed that mite egg production and its changes following mite herbivory changed depending on the AMF species. In addition, Principal component analysis for leaf chemicals revealed not only mite-induced changes in leaf chemical composition, but also AMF effects on the herbivore-induced response in a species-specific way. Thus, we need to pay more attention to the species identity of AMF as an important factor in determining the strength of effects of belowground AMF on the performance and/or preferences of aboveground herbivores.

Periodic Solutions of a Viscous Gas Equation

Publisher Summary This chapter discusses the periodic solutions of a viscous gas equation. It considers the one-dimensional motion of viscous gas on a finite interval. When the gas is assumed barotropic or polytropic, it is known by Kanel and Kazhikhov that the initial boundary value problem with fixed boundary has the unique global in time solution which decays to the constant equilibrium state as time tends to infinity. While in the case the time-dependent external force or the piston acts on the gas, the obtained global in time solution has only the bound which depends on time so that the asymptotic behavior in time is not known. This chapter considers the isothermal gas motion under the time-dependent external force or under the moving boundary condition.