Euler Equation

The Euler equation, a fundamental equation in fluid dynamics, describes the motion of inviscid fluids. Current research focuses on understanding complex fluid behaviors, including the existence of solutions exhibiting finite-time blow-up, and exploring novel computational approaches such as neural networks and geometric mechanics to solve and analyze these equations, particularly in high-dimensional or constrained systems. These investigations are crucial for advancing our understanding of fluid dynamics and have implications for diverse applications, ranging from spacecraft control to the design of more efficient computational fluid dynamics solvers.