Mathematical Foundations of Fluid Dynamics

Our definitive objective is the examination on the hypothesis of oil, which is crucial in lessening the grinding - the most significant test of the individual in the 21st century. Toward the beginning we experienced some ambiguity of the present method for exhibiting results on fluid elements. \cite{Kh}, \cite{SO}, \cite{TK} and so on. Right now might want to clarify some of them. We will show that by the utilization of chain rule, the Euler's type of speed vectors is clarified. The principle oddity of our technique is a successful utilization of differential structures combined with the general type of Stokes' hypothesis to make numerous outcomes in fluid mechanics easier. Specifically, we will explain the thought of disparity and course in the $3$-dimensional flow case in Theorem \ref{thm3.1divcurl}. Further on account of $2$-dimensional flow by the utilization of complex analysis, we restore the outcomes in that hypothesis. For fulfillment we collect some fundamental outcomes from the hypothesis of complex capacities, cf. for example \cite{CKT}. We express some essential notable outcomes from mathematical analysis for simple reference and independent nests.