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.

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A systematic design procedure has been developed for analyzing the blast resistance of clamped sandwich beams. The structural response of the sandwich beam is split into three sequential steps: stage I is the one-dimensional fluid-structure interaction problem during the blast loading event, and results in a uniform velocity of the outer face sheet; during stage II the core crushes and the velocities of the faces and core become equalized by momentum sharing; stage III is the retardation phase over which the beam is brought to rest by plastic bending and stretching. The third-stage analytical procedure is used to obtain the dynamic response of a clamped sandwich beam to an imposed impulse. Performance charts for a wide range of sandwich core topologies are constructed for both air and water blast, with the monolithic beam taken as the reference case. These performance charts are used to determine the optimal geometry to maximize blast resistance for a given mass of sandwich beam. For the case of water blast, an order of magnitude improvement in blast resistance is achieved by employing sandwich construction, with the diamond-celled core providing the best blast performance. However, in air blast, sandwich construction gives only a moderate gain in blast resistance compared to monolithic construction.

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