Explore the first lecture in a series on Wavelet-inspired Nash's iteration, delivered by Hyunju Kwon at the International Centre for Theoretical Sciences. Delve into advanced mathematical concepts related to fluid dynamics, focusing on the analysis of Euler and Navier-Stokes equations. Learn about recent breakthroughs in fluid mechanics research, including the resolution of Onsager's conjecture and new techniques in statistical hydrodynamics. Gain insights into nonlinear partial differential equations and their applications in physics, engineering, finance, and biology. Suitable for PhD students, postdocs, and faculty members working on mathematical aspects of fluid flow equations.