Newton's problem : a smooth minimum method

Newton's problem consists in minimizing the resistance of a fluid on a body. It has been proposed by Sir Isaac Newton in 1685 and has been widely studied since. Yet, the optimal solution is still unknown. Many numerical and analytical methods were tested and some of them provided excellent results. In this thesis, we propose a new method to solve Newton's problem based on the analysis of the previous work of the literature. It uses the smooth minimum function, namely, the LogSumExp function. Its smoothness allows in some sense to easily evaluate and optimize the resistance of the body. However, the method suffers from technical difficulties. At the end, the method provides bodies with similar properties than the bodies obtained in the literature. In particular, the best resistances of the literature are around 0.4% better than our results obtained with the smooth method.