In this paper, we present a review of featured works in the field of hydrodynamics with the main aim to clarify the ways of understanding the algorithms for solving the Navier–Stokes equations. Discussing the existing algorithms, approaches and analytical or semi-analytical methods, we especially note that important problems of stability for the exact solutions should be explored accordingly relate to this respect, e.g. exploring the case of non-stationary helical flows of the Navier–Stokes equations for incompressible fluids with variable (spatially dependent) coefficient of proportionality α between velocity and the curl field of the flow. Meanwhile, the system of Navier–Stokes equations (including continuity equation) has been successfully explored previously with respect to the existence of analytical way for presentation of non-stationary helical flows of the aforementioned type. Conditions for the stability criteria of the exact solution for such the type of flows are obtained herein in the current research, for which non-stationary helical flow with invariant Bernoulli-function is considered.

The present review analyzes classes of exact solutions for the convection and thermal diffusion equations in the Boussinesq approximation. The exact integration of the Oberbeck–Boussinesq equations for convection and thermal diffusion is more difficult than for the Navier–Stokes equations. It has been shown that the exact integration of the thermal diffusion equations is carried out in the Lin–Sidorov–Aristov class. This class of exact solutions is a generalization of the Ostroumov–Birikh family of exact solutions. The use of the class of exact solutions by Lin–Sidorov–Aristov makes it possible to take into account not only the inhomogeneity of the pressure field, the temperature field and the concentration field, but also the inhomogeneous velocity field. The present review shows that there is a class of exact solutions for describing the flows of incompressible fluids, taking into account the Soret and Dufour cross effects. Accurate solutions are important for modeling and simulating natural, technical and technological processes. They make it possible to find new physical mechanisms of momentum transfer for the design of new types of equipment.

In this short communication, we review seven applications of NFL that we have explored in a number of papers: (1) Background: the purpose of this study is to review how neutrosophic logic can be found useful in a number of diverse areas of interest; (2) Methods: we use logical analysis based on NL; (3) Results: some fields of study may be found elevated after analyzed by NL theory; and (4) Conclusions: we can expect NL theory to be applied in many areas of research too, in applied mathematics, economics, and physics. Hopefully the readers will find a continuing line of thoughts in our research from the last few years.

In an era where innovation is not just about solving problems but also about enhancing human experiences and fostering personal fulfillment, the convergence of Ikigai principles with Design Thinking methodology offers a promising avenue for holistic problem-solving and innovation. This paper explores the intersection of Ikigai—a Japanese concept representing one's reason for being—and Design Thinking—a human-centered approach to innovation. We propose a conceptual framework, termed Ikigai-Driven Design (IDD), which integrates the principles of Ikigai with the stages of Design Thinking. IDD comprises five main stages: Empathize, Define, Ideate, Prototype, and Test, each combining elements of Ikigai and Design Thinking to foster purposeful innovation. The Empathize stage emphasizes understanding what users love and what the world needs, drawing insights from human-centered research methods. In the Define stage, practitioners frame problems through the lens of Ikigai, aligning identified needs with their own passions and strengths. The Ideate stage encourages divergent thinking, leveraging practitioners' Ikigai to generate creative solutions. Prototypes created in the Prototype stage embody practitioners' purpose and values, tested and refined based on user feedback in the Test stage. By integrating Ikigai principles with Design Thinking methodology, IDD offers a structured yet flexible approach to innovation that resonates deeply with users and contributes to practitioners' sense of fulfillment and meaning.