This article deals with a survey of the Newtonian fluid dynamics equations with some historical notes and a discussion related to the solvability of fluid flows problems. On the way, we discuss briefly various questions related with the behavior of fluid flows governed by these fluid dynamics equations. Some of these questions are, in fact, closely connected with the well-posedness of fluid dynamics problems. We touch on the problem of the fluid dynamics limit of the Boltzmann equation of the kinetic theory of gases. An overview of some rigorous recent results on the existence and uniqueness of solutions of the fluid flows problems concludes this paper. At the end, after some concluding remarks, there are 306 references.

In this paper the plane elasticity problem for a nonhomogeneous medium containing a crack is considered. It is assumed that the Poisson's ratio of the medium is constant and the Young's modulus E varies exponentially with the coordinate parallel to the crack. First the half plane problem is formulated and the solution is given for arbitrary tractions along the boundary. Then the integral equation for the crack problem is derived. It is shown that the integral equation having the derivative of the crack surface displacement as the density function has a simple Cauchy type kernel. Hence, its solution and the stresses around the crack tips have the conventional square-root singularity. The solution is gi.ven for various loading conditions. The results show that the effect of the Poisson's ratio and consequently that of the thickness constraint on the stress intensity factors are rather negligible. On the other hand, the results are highly affected by the parameter a describing the material nonhomogeneity in E{x} = Eoexp(sx).

In this paper the crack problem for two bonded dissimilar homogeneous elastic half-planes is considered. It is assumed that the interfacial region can be modeled by a very thin layer of nonhomogeneous material. Even though the formulation given is rather general, in the particular model used the elastic properties of the interfacial layer are assumed to vary continuously between that of the two semi-infinite planes. The layer is assumed to have a series of collinear cracks parallel to the nominal interface. The related mixed boundary problem is formulated for arbitrary crack surface tractions which can be used to accommodate any general external loading condition through a proper superposition. A single crack problem for two different material combinations is solved as examples, and Modes I and II stress-intensity factors, the energy release rate and the direction of a probable crack growth are calculated.

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In this paper the general plane strain problem of adhesively bonded structures which consist of two different orthotropic adherends ;s considered. Assuming that the thicknesses of the adherends are constant and are small in relation to the lateral dimensions of the bonded region, the adherends are treated as plates. Also, assuming that the thickness of the adhesive is small compared to that of the adherends, the thickness variation of the stresses in the adhesive layer is neglected. However, the transverse shear effects in the adherends and the in-plane normal strain in the adhesive are taken into account. The problem is reduced to a system of differential equations for the adhesive stresses which is solved ;n closed form. A single lap joint and a stiffened plate under various loading conditions are considered as examples. To verify the basic trend of the solutions obtained from the plate theory and to give some idea about the validity of the plate assumption itself, a sample problem is solved by using the finite element method and by treating the adherends and the adhesive as elastic continua. It is found that the plate theory used in the analysis not only predicts the correct trend for the adhesive stresses but also gives rather surprisingly accurate results. The solution is obtained by assuming linear stress-strain relations for the adhesive. In the Appendix the problem is formulated by using a nonlinear material for the adhesive and by following two different approaches.